Дисертації з теми "Black hole waves"

Gravitational-waves provide a unique probe of the stellar remnants---black holes and neutron stars---left behind at the end of massive stars lives. On the 14th September 2015 the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) made the first direct detection of gravitational waves from a merging stellar mass binary black hole, GW150914, during its first observation run (O1). In this thesis we present Compact Object Mergers: Population Astrophysics and Statistics (COMPAS). COMPAS is a platform incorporating astrophysical modelling tools and statistical analysis tools to extract information from the population of merging binary black holes we observe. We demonstrate that the masses, spins and observed rate of binary black holes can offer new insights into their formation.

The revolutionary discoveries of the last few years have opened a new era of astronomy. With the detection of gravitational-waves, we now have the opportunity of investigating new phenomena, such as mergers of black-holes. Furthermore, multi-messenger observations now allow us to combine information from different channels, providing insight into the physics involved. With this rapid evolution and growth of the field, many challenges need to be faced. In this thesis we propose three data analysis strategies to efficiently study the coalescences of compact binaries. First we propose an algorithm to reduce the computational cost of Bayesian inference on gravitational-wave signals. Second we prove that machine-learning signal classification could enhance the significance of gravitational-wave candidates in unmodelled searches for transients. Finally we develop a tool, saprEMo, to predict the number of electromagnetic events, which according to a specific emission model, should be present in a particular survey.

The main purpose of this work is to study the collision of two black holes and the energy loss due to the gravitational waves emitted during this collision in the framework of general relativity. For this purpose we first study plane wave geometries and their collisions. More realistic collisions are the pp-wave collisions. As an analytic treatment of this problem, we investigate the head-on collision of two ultra-relativistic black holes. Treating the problem perturbatively, we extract the news function to compute how much energy is radiated in gravitational waves during the process. We show that the news function vanishes for the solutions obtained meaning that there is no mass-loss at the order of approximation.

Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2009.
Title from electronic title page (viewed Jun. 26, 2009). "...in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics and Astronomy." Discipline: Physics and Astronomy; Department/School: Physics and Astronomy.

Black holes have many faces. Arguably, they are the most interesting objects in theoretical physics, revealing the elusive connection between gravity and quantum mechanics. Within the gauge/string duality they provide useful insights on strongly coupled quantum field theories and on quantum gravity. Furthermore, probing the strong curvature regime of any gravity theory, black holes carry the imprint of possible strong curvature corrections to General Relativity. Finally, beside their unique theoretical properties, several experimental evidences suggest that astrophysical black holes exist in nature and they are believed to be very common objects in the universe. In this dissertation we discuss several applications of linear perturbation theory in black hole physics. As applications in theoretical physics, we study perturbations of dilatonic black holes in Einstein-Maxwell theory and the holographic properties of the dual field theory via the Anti de Sitter/Condensed Matter duality. Furthermore we discuss a method to compute long-lived quasinormal modes of Schwarzschild-Anti de Sitter black holes and we study vortex black hole solutions in three dimensional Anti de Sitter gravity. As applications in astrophysics, we discuss how the characteristic oscillations of black holes in string-inspired theories of gravity can provide observable signatures of deviations from General Relativity. We study two well-motivated effective theories: Dynamical Chern-Simons gravity and Einstein-Dilatonic-Gauss-Bonnet gravity. We conclude by discussing the black hole paradigm. Motivated by the lacking of a definitive answer on the existence of astrophysical black holes, we study some viable alternatives, generally called “black hole mimickers”. We focus on two representative cases: static thin-shell gravastars and superspinars. We discuss their stability, gravitational-wave signature and viability as astrophysical objects.

I study linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes. In the first part of this thesis two decay results are proven for general finite energy solutions to the linear wave equation on higher dimensional Schwarzschild black holes. I establish uniform energy decay and improved interior first order energy decay in all dimensions with rates in accordance with the 3 + 1-dimensional case. The method of proof departs from earlier work on this problem. I apply and extend the new physical space approach to decay of Dafermos and Rodnianski. An integrated local energy decay estimate for the wave equation on higher dimensional Schwarzschild black holes is proven. In the second part of this thesis the global study of solutions to the linear wave equation on expanding de Sitter and Schwarzschild de Sitter spacetimes is initiated. I show that finite energy solutions to the initial value problem are globally bounded and have a limit on the future boundary that can be viewed as a function on the standard cylinder. Both problems are related to the Cauchy problem in General Relativity.

The inspiral and merger of two black holes is among the most exciting and extreme events in our universe. Being one of the loudest sources of gravitational waves, they provide a unique dynamical probe of strong-field general relativity and a fertile ground for the observation of fundamental physics. While the detection of gravitational waves alone will allow us to observe our universe through an entirely new window, combining the information obtained from both gravitational wave and electro-magnetic observations will allow us to gain even greater insight in some of the most exciting astrophysical phenomena. In addition, binary black-hole mergers serve as an intriguing tool to study the geometry of space-time itself. In this dissertation we study the merger process of binary black-holes in a variety of conditions. Our results show that asymmetries in the curvature distribution on the common apparent horizon are correlated to the linear momentum acquired by the merger remnant. We propose useful tools for the analysis of black holes in the dynamical and isolated horizon frameworks and shed light on how the final merger of apparent horizons proceeds after a common horizon has already formed. We connect mathematical theorems with data obtained from numerical simulations and provide a first glimpse on the behavior of these surfaces in situations not accessible to analytical tools. We study electro-magnetic counterparts of super-massive binary black-hole mergers with fully 3D general relativistic simulations of binary black-holes immersed both in a uniform magnetic field in vacuum and in a tenuous plasma. We find that while a direct detection of merger signatures with current electro-magnetic telescopes is unlikely, secondary emission, either by altering the accretion rate of the circumbinary disk or by synchrotron radiation from accelerated charges, may be detectable. We propose a novel approach to measure the electro-magnetic radiation in these simulations and find a non-collimated emission that dominates over the collimated one appearing in the form of dual jets associated with each of the black holes. Finally, we provide an optimized gravitational wave detection pipeline using phenomenological waveforms for signals from compact binary coalescence and show that by including spin effects in the waveform templates, the detection efficiency is drastically improved as well as the bias on recovered source parameters reduced. On the whole, this disseration provides evidence that a multi-messenger approach to binary black-hole merger observations provides an exciting prospect to understand these sources and, ultimately, our universe.
Schwarze Löcher gehören zu den extremsten und faszinierensten Objekten in unserem Universum. Elektromagnetische Strahlung kann nicht aus ihrem Inneren entkommen, und sie bilden die kompaktesten Objekte, die wir kennen. Wir wissen heute, dass in den Zentren der meisten Galaxien sehr massereiche schwarze Löcher vorhanden sind. Im Fall unserer eigenen Galaxie, der Milchstrasse, ist dieses schwarze Loch ungefähr vier Millionen mal so schwer wie unsere Sonne. Wenn zwei Galaxien miteinander kollidieren, führt dies auch dazu, dass ihre beiden schwarzen Löcher kollidieren und zu einem einzelnen schwarzen Loch verschmelzen. Das Simulieren einer solchen Kollision von zwei schwarzen Löchern, die Vorhersage sowie Analyse der von ihnen abgestrahlten Energie in Form von Gravitations- und elektromagnetischen Wellen, bildet das Thema der vorliegenden Dissertation. Im ersten Teil dieser Arbeit untersuchen wir die Verschmelzung von zwei schwarzen Löchern unter verschiedenen Gesichtspunkten. Wir zeigen, dass Ungleichmässigkeiten in der Geometrie des aus einer Kollision entstehenden schwarzen Loches dazu führen, dass es zuerst beschleunigt und dann abgebremst wird, bis diese Ungleichmässigkeiten in Form von Gravitationswellen abgetrahlt sind. Weiterhin untersuchen wir, wie der genaue Verschmelzungsprozess aus einer geometrischen Sicht abläuft und schlagen neue Methoden zur Analyse der Raumzeitgeometrie in Systemen vor, die schwarze Löcher enthalten. Im zweiten Teil dieser Arbeit beschäftigen wir uns mit den Gravitationswellen und elektromagnetischer Strahlung, die bei einer Kollision von zwei schwarzen Löchern freigesetzt wird. Gravitationswellen sind Wellen, die Raum und Zeit dehnen und komprimieren. Durchläuft uns eine Gravitationswelle, werden wir in einer Richtung minimal gestreckt, während wir in einer anderen Richtung minimal zusammengedrückt werden. Diese Effekte sind allerdings so klein, dass wir sie weder spüren, noch auf einfache Weise messen können. Bei einer Kollision von zwei schwarzen Löchern wird eine grosse Menge Energie in Form von Gravitationswellen und elektromagnetischen Wellen abgestrahlt. Wir zeigen, dass beide Signale in ihrer Struktur sehr ähnlich sind, dass aber die abgestrahlte Energie in Gravitationswellen um ein Vielfaches grösser ist als in elektromagnetischer Strahlung. Wir führen eine neue Methode ein, um die elektromagnetische Strahlung in unseren Simulationen zu messen und zeigen, dass diese dazu führt, dass sich die räumliche Struktur der Strahlung verändert. Abschliessend folgern wir, dass in der Kombination der Signale aus Gravitationswellen und elektromagnetischer Strahlung eine grosse Chance liegt, ein System aus zwei schwarzen Löchern zu detektieren und in einem weiteren Schritt zu analysieren. Im dritten und letzen Teil dieser Dissertation entwickeln wir ein verbessertes Suchverfahren für Gravitationswellen, dass in modernen Laser-Interferometerexperimenten genutzt werden kann. Wir zeigen, wie dieses Verfahren die Chancen für die Detektion eines Gravitationswellensignals deutlich erhöht, und auch, dass im Falle einer erfolgreichen Detektion eines solchen Signals, seine Parameter besser bestimmt werden können. Wir schliessen die Arbeit mit dem Fazit, dass die Kollision von zwei schwarzen Löchern ein hochinteressantes Phenomenon darstellt, das uns neue Möglichkeiten bietet die Gravitation sowie eine Vielzahl anderer fundamentaler Vorgänge in unserem Universum besser zu verstehen.

This thesis describes the results of the experimental investigations into some new geometrical configurations in plate-like structures materialising one-dimensional (1D) acoustic black holes for flexural waves (wedges of power-law profile) and two-dimensional (2D) acoustic black holes for flexural waves (circular indentations of power-law profile). Such acoustic black holes allow the user to reduce the amplitudes of the vibration responses of plate-like structures to a maximum effect, while not increasing the mass of the structures. This thesis also suggests some new real world practical applications for this damping technique. Initially, the effects of geometrical and material imperfections on damping flexural vibrations in plates with attached wedges of power-law profile (1D black holes) were investigated, demonstrating that this method of damping is robust enough for practical applications. Then, damping of flexural vibrations in turbofan blades with trailing edges tapered according to a power-law profile has been investigated. In addition, experimental investigations into power-law profiled slots within plates have been also conducted. Another important configuration under investigation was that of circular indentations (pits) of power-law profile within the plate. In the case of quadratic or higher-order profiles, such indentations materialise 2D acoustic black holes for flexural waves. To increase the damping efficiency of power-law profiled indentations, the absorption area has been enlarged by increasing the size of the central hole in the pit, while keeping the edges sharp. The next step of investigation in this thesis was using multiple indentations of power-law profile (arrays of 2D black holes). It was shown that not only do multiple indentations of power-law profile provide substantial reduction in the damping of flexural vibrations, but also a substantial reduction in radiated sound power. The experimental results have been obtained also for a cylindrical plate incorporating a central hole of quadratic profile. They are compared to the results of numerical predictions, thus validating the results and the experimental technique. Investigations into the effects of indentations of power-law profile made in composite plates and panels and their subsequent inclusion into composite honeycomb sandwich panels are also reported. These indentations again act as 2D acoustic black holes for flexural waves and they effectively damp flexural vibrations within the panels. It was also demonstrated that these indentations can be enclosed in smooth surfaced panels and that no additional damping layer is required to induce the acoustic black hole effect in composite structures. In conclusion, it has been confirmed in this thesis that one and two-dimensional acoustic black holes represent an effective method of damping flexural vibrations and reducing the associated structure-borne sound. Furthermore, this thesis has shown that acoustic black holes can be efficiently employed in practical applications, such as trailing edges of jet engine fan blades, composite panels, and composite honeycomb sandwich structures.

本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものである
Kyoto University (京都大学)
0048
新制・課程博士
博士(理学)
甲第5895号
理博第1602号
新制||理||893(附属図書館)
UT51-95-D214
京都大学大学院理学研究科物理学第二専攻
(主査)教授 佐藤 文隆, 教授 益川 敏英, 教授 九後 太一
学位規則第4条第1項該当

Le contrôle des vibrations à basse fréquence adapté aux structures légères est un défi scientifique ettechnologique en raison de contraintes économiques et écologiques de plus en plus strictes. De récentes études enacoustique ont portées sur l’absorption totale d’ondes basses fréquences à l’aide d’absorbeurs parfaits sublongueursd’onde. Ces métamatériaux sont obtenus en exploitant la condition de couplage critique. Unegénéralisation de cette méthode pour le domaine élastodynamique serait d’un grand intérêt pour répondre auxexigences du contrôle des vibrations de structures légères à basse fréquence.Cette thèse vise à adapter le problème d’absorption parfaite des ondes de flexion dans des systèmes 1D et 2D avecdes résonateurs locaux en utilisant la condition de couplage critique. Une étude préliminaire sur des systèmes 1D àgéométries simples sont d’abord proposée. Celle-ci propose une méthode de conception de résonateurs simplespour une absorption efficace des ondes de flexion. Une complexification du système 1D est ensuite considérée avecl’étude du couplage critique de Trou Noir Acoustique (TNA) 1D. Ceci a motivé l’interprétation de l’effet TNA à l’aidedu concept de couplage critique afin de présenter des outils clés à de futures procédures d’optimisation pour ce typede terminaisons. La condition de couplage critique est ensuite étendue aux systèmes 2D. L’absorption parfaite parle premier mode axisymétrique d’un résonateur circulaire inséré dans une plaque mince infinie est analysée. Ladiffusion multiple par une ligne de résonateurs circulaires insérés dans une plaque mince 2D infinie ou semi-infinie,appelée métaplaque, est aussi considérée dans l’optique de se rapprocher d’une application industrielle. A traverscette thèse, des modèles analytiques, des simulations numériques et des expériences sont présentés pour valider lecomportement physique des systèmes présentés
The vibration control adapted to light structures is a scientific and technological challenge due toincreasingly stringent economic and ecological standards. Meanwhile, recent studies in audible acoustics havefocused on broadband wave absorption at low frequencies by means of subwavelength perfect absorbers. Suchmetamaterials can totally absorb the energy of an incident wave. The generalisation of this method for applicationsin elastodynamics could be of great interest for the vibration control of light structures.This thesis aims at adapting the perfect absorption problem for flexural waves in 1D and 2D systems with localresonators using the critical coupling condition. A study of 1D systems with simple geometries is first proposed. Thisprovides methods to design simple resonators for an effective absorption of flexural waves. The 1D systems thenbecome more complex by studying the critical coupling of 1D Acoustic Black Holes (ABH). The ABH effect is theninterpreted using the concept of critical coupling, and key features for future optimisation procedures of ABHs arepresented. The critical coupling condition is then extended to 2D systems. The perfect absorption by the firstaxisymmetric mode of a circular resonator inserted in a thin plate is analysed. Multiple scattering by an array ofcircular resonators inserted in an infinite or semi-infinite 2D thin plate, called metaplate, is also considered to getclose to practical applications. Through this thesis, analytical models, numerical simulations and experiments areshown to validate the physical behaviour of the systems presented

This project contains an exposition of the basics of General Relativity up to the study of Gravitational Waves. The goal is to apply this theory to understand binary systems, how they generate gravitational waves and the energy they lose in doing so. Gravitational waves have been a topic of interest in relativity ever since their theoretical prediction in 1916. Now the interest in the subject has been renewed since LIGO's announcement of the first detection of gravitational waves, proving once again the power of General Relativity. This topic is very promising because of its implications in the future of astronomy and cosmology as a new method to obtain information about our universe.

Cette thèse s'inscrit dans le cadre de la modélisation des ondes gravitationnelles et du mouvement relativiste associés aux systèmes binaires à grand rapport de masses (Extreme Mass Ratio Inspiral - EMRI). Ces systèmes sont formés d'un trou noir super massif autour duquel gravite un objet compact de masse stellaire. Dans le formalisme de la théorie perturbative des trous noirs, on développe une méthode numérique qui calcule les formes d'ondes produites par une particule ponctuelle en orbite autour d'un trou noir de Schwarzschild. Il s'agit de résoudre l'équation d’onde de Regge-Wheeler-Zerilli dans le domaine temporel dont la solution, invariante de jauge, peut être reliée aux modes de polarisation, à l'énergie et au moment cinétique emporté par les ondes gravitationnelles. En réaction à l'énergie et au moment perdu, la trajectoire de la particule est affectée au cours du temps. Dans le cadre du formalisme de MiSATaQuWa, on calcule la force propre agissant sur une particule, initialement au repos, est en chute libre sur un trou noir de Schwarzschild. Nous montrons comment cette quantité est définie dans la jauge de Regge-Wheeler par le biais de la régularisation mode-sum. L'effet de la force propre sur le mouvement de la particule est ensuite pris en compte de façon itérative et auto-consistante grâce à un algorithme utilisant une méthode d'orbites osculatrices que nous avons développé. Nous quantifions cet effet en calculant soit la déviation orbitale par rapport au mouvement géodésique, soit les formes d'ondes perturbées et l'énergie rayonnée associée
This thesis focuses on modelling the gravitational waves and the relativistic motion associated to Extreme Mass Ratio Inspiral (EMRI) systems. These systems consist of a stellar mass compact object gravitationally captured by a super-massive black hole. In black hole perturbation theory, we further develop a numerical method which computes waveforms generated by a point mass particle orbiting a Schwarzschild black hole. The Regge-Wheeler-Zerilli wave equation is solved in time domain. The gauge invariant solution is related to the polarisation modes, the energy and the angular momentum carried by the gravitational waves. In reaction to the energy and the moment lost, the trajectory is modified all along. In the MiSaTaQuWa formalism, we compute the self-force acting upon a point particle which is initially at rest, and then falling into a Schwarzschild black hole. We show how this quantity is defined in the Regge-Wheeler gauge by using the mode-sum regularisation technique. We take into account the self-force effect on the motion of the particle by using an iterative and osculating orbit method conceived herein. We quantify the orbital deviation with respect to the geodesic motion, but also the perturbed wave forms and the associated radiated energy

This thesis concerns the use of observations of gravitational waves as tools for astronomy and fundamental physics. Gravitational waves are small ripples in spacetime produced by rapidly accelerating masses; their existence has been predicted for almost 100 years, but the first direct evidence of their existence came only very recently with the announcement in February 2016 of the detection by the LIGO and VIRGO collaborations. Part I of this thesis presents an introduction to gravitational wave astronomy, including a detailed discussion of a wide range of gravitational wave sources, their signal morphologies, and the experimental detectors used to observe them. Part II of this thesis concerns a particular data analysis problem which often arises when trying to infer the source properties from a gravitational wave observation. The use of an inaccurate signal model can cause significant systematic errors in the inferred source parameters. The work in this section concerns a proposed technique, called the Gaussian process marginalised likelihood, for overcoming this problem. Part III of this thesis concerns the possibility of testing if the gravitational field around an astrophysical black hole conforms to the predictions of general relativity and the cosmic censorship hypothesis. It is expected that the gravitational field should be well described by the famous Kerr solution. Two approaches for testing this hypothesis are considered; one using X-ray observations and one using gravitational waves. The results from these two approaches are compared and contrasted. Finally, the conclusions and a discussion of future prospects are presented in part IV of this thesis.

A colisão de buracos negros é uma das fontes mais importantes de ondas gravitacionais e, em geral, a emissão anisotrópica da radiação causa um recuo do objeto final. Este cenário já é conhecido há décadas, mas foi somente com o recente avanço na relatividade numérica que as velocidades finais dos objetos radiantes foram computadas com precisão. Os valores encontrados podem ser altos o suficiente para exercerem um importante papel no crescimento de buracos negros super massivos via coleção de galáxias e na abundância de núcleos galáticos ativos contendo buracos negros. Este é um autêntico efeito da não linearidade de Relatividade Geral e esta tese fornece uma nova metodologia estudar alguns aspectos da dinâmica da colisão de buracos negros. Consideramos o horizonte como uma tela canônica que codifica as informações da evolução temporal do espaço-tempo. Com esta hipótese, fenômenos como o anti-kick, isto é, uma súbita desaceleração do sistema antes de atingir a velocidade final, são explicado em termos da dissipação das deformações do horizonte. Estudamos primeiramente o Espaço-tempo de Robinson-Trautman. Uma das solução mais simples das equações de Einstein, esta métrica nos fornece um poderoso modelo para investigar tanto a perda de massa quanto o recuo do objeto final. Mostramos que, quando as configurações iniciais tem simetria especular, a massa do buraco negro remanescente e a energia irradiada são completamente determinadas pela condição inicial. Com isso, obtemos as expressões analíticas dos resultados numéricos obtidos anteriormente na literatura. Além disto, com o auxilio do método espectral de Galerkin, analisamos o regime não linear das equações envolvidas e verificamos que se pode estimar a velocidade de recuo final com boa precisão a partir de medidas da assimetria da condição inicial. Introduzimos na seqüência a curvatura efetiva como uma medida das deformações intrínsecas ao horizonte. Além de considerar as deformações gerais, ela também inclui as diferenças entre os hemisférios norte e sul. No espaço-tempo de Robinson-Trautman, essa quantidade se correlaciona de uma forma injetora com a velocidade final. Para superar algumas limitações dessa solução, aplicamos o mesmo procedimento nos resultados da simulação numérica de uma colisão head-on. Neste caso, a curvatura efetiva, está na realidade, correlacionada com a aceleração do sistema. Refinamentos e generalizações desta técnica são também discutidos e propostos para trabalhos futuros.
Colliding black holes are one of the most important sources of gravitational waves and the anisotropic emission of the radiation generally causes the recoil of the final hole. This scenario has been known for decades, but it is only thanks to the recent progress in numerical relativity that the final velocity have been accurately computed. The values found can be large enough to play an important role in the growth of supermassive black holes via mergers of galaxies and on the number of galaxies containing them. This is a genuine nonlinear effect of general relativity and this thesis provides a new methodology to study some features on the dynamics of the collision. We propose that the horizon is a canonical screen, which encodes he information of its surroundings. With this assumption, phenomena such as the anti-kick, namely the sudden deceleration before reaching the final velocity, are explained in terms of the dissipation of the horizons deformation. We first study the Robinson-Trautman spacetime. One of the simplest solutions of Einsteins equations, it provides us with a powerful toymodel to investigate both the mass loss of the system and the recoil of the final object. We show that, for the case of reflectionsymmetric initial configurations, the mass of the remnant black-hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some numerical results that had appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the non-linear regime of the equations involved, we found that the recoil velocity can be estimated with good accuracy from some symmetry measures of the initial data. Then we introduce the effective urvature as a measure of intrinsic deformations on the horizon. Not only does it account for overall deformation, but also for the differences on the north and south hemispheres. In the Robinson-Trautman spacetime, this quantity correlates in an injective way with the final velocity. To overcome some caveats of this solutions, we apply the same procedure to the results given by numerical simulations of a head-on collision. In the case, the effective curvature is actually correlated with the acceleration of the system. Further improvement and generalizations of this technic is also discussed and proposed for future work.

This thesis studies the propagation of fundamental fields on black hole and black hole analogue spacetimes. We consider the scalar, electromagnetic, gravitational and Dirac fields, and their governing equations, in various scenarios. We initially consider an analogue gravity model, the draining bathtub vortex, that shares features with the Kerr black hole, such as a horizon and an ergoregion. We solve the wave equation approximately, via the eikonal approximation, and numerically, using the method of lines, and show that a point-like disturbance maps out the lightcone of the effective spacetime. The Schwarzschild and Kerr black hole spacetimes are then introduced and we discuss their key features. We solve the scalar wave equation for the black hole spacetimes and compare with the analogue spacetime. We then introduce the self force, the back reaction of a body's own field on its motion. The scalar self force on Kerr spacetime is calculated using the worldline integration method. This involves solving the scalar wave equation to find the Green function via the Kirchhoff representation and integrating over the entire past history of the worldline. The electromagnetic (EM) self force is calculated via the mode sum method. We use both analytical and numerical techniques to calculate EM self force for a particle held static outside of a Schwarzschild black hole. The gauge freedom of the gravitational self force is also discussed. We construct for eccentric orbits on Schwarzschild the spin precession invariant, a gauge invariant quantity. We compare the spin precession invariant calculated using numerical self force data with a post-Newtonian calculation. Finally we investigate the Dirac (fermionic) field in searching for the existence of bound states. We find that the solutions which satisfy the boundary conditions, obey a three-term recurrence-relation. Using continued-fraction methods we find a spectrum of quasi-bound states of the Dirac field exists.

Gravitation is a manifestation of the space-time curvature and gravitational waves aredistortions traveling through the fabric of space-time. Scientists have tried to detectgravitational waves for decades, but the first direct detection of gravitational waves andthe first observation of a binary black hole merger was made in 2015. The purpose ofthis report is to introduce General Relativity and binary black holes and to calculate thetime to coalescence of two back holes with circular or elliptical orbits. We find that abinary black hole in an elliptical orbit with large eccentricity coalesces faster than in acircular orbit.

Gravitation is a manifestation of the space-time curvature and gravitational waves aredistortions traveling through the fabric of space-time. Scientists have tried to detectgravitational waves for decades, but the first direct detection of gravitational waves andthe first observation of a binary black hole merger was made in 2015. The purpose ofthis report is to introduce General Relativity and binary black holes and to calculate thetime to coalescence of two back holes with circular or elliptical orbits. We find that abinary black hole in an elliptical orbit with large eccentricity coalesces faster than in acircular orbit.

This thesis deals with three aspects of modern astrophysical research. We propose a Bayesian data analysis framework to test alternative theories of gravity using observations of Gravitational Waves (GWs) from the inspiral phase of binary systems. We compare General Relativity predictions to the ones from a Massive Graviton theory. We can discriminate between the two theories and produce posterior probability distribution functions. We also devise a method to combine multiple observations that y increases the amount of information that is possible to extract from GWs. Using current wide-field sky survey s, in concert with the established Luminosity -- Black Hole mass relation, we calculate the mass distribution of supermassive massive black holes (SMBHs) and Active Galactic Nuclei (AGNs) in three different environments. SMBHs and radio-AGNs are concentrated in dense environments. The Black Hole Fundamental Plane predicts X-ray properties for our SMBHs and unifies modes of AGN activity in terms of the rate of accretion. Studying two-body mergers of realistic galaxy clusters, we show that these reproduce the observed metallicity distribution in the Intra Cluster Medium (ICM). We characterise entropy generation and mixing induced by the merger process.

Avec la naissance de l’"astronomie gravitationnelle", vient l’opportunité inédite de tester la relativité générale et ses alternatives dans un régime de champ fort jamais observé jusqu’alors : celui de la coalescence d’un système binaire d’objets compacts. Cette thèse propose d’étudier le problème du mouvement ainsi que du rayonnement gravitationnel d’un tel système en gravités modifiées, en y adaptant et en généralisant certains développements analytiques clés de la relativité générale. On montre d’abord comment étendre le formalisme "effective-one-body" (EOB) à une large classe de gravités modifiées, parmi lesquelles les théories scalaire-tenseur. Dans ces dernières, l’interaction gravitationnelle est modifiée par l’ajout d’un degré de liberté scalaire (sans masse) à la relativité générale. Le lagrangien à deux corps correspondant étant connu à l’ordre post-post-keplerien, nous construisons un hamiltonien EOB associé, décrivant le mouvement d’une particule test dans des champs effectifs. Ceci permet de simplifier la dynamique à deux corps et d’en définir une resommation ; et ainsi, d’en explorer le régime de champ fort, près de la coalescence du système. On "s’attaque" ensuite, et pour la première fois, à la description analytique d’un système binaire de trous noirs "chevelus", afin d’obtenir les formes d’ondes gravitationnelles (EOB) associées ; et ce, sur l’exemple simple des théories Einstein-Maxwell-dilaton, qui généralisent les théories scalaire-tenseur par l’ajout d’un champ vectoriel (sans masse). Pour ce faire, on calcule le lagrangien à deux corps à l’ordre post-keplerien ainsi que le flux d’énergie rayonnée à l’infini à l’ordre quadrupolaire. Tout comme en relativité générale, ces développements reposent sur la description de la trajectoire des trous noirs par les lignes d’univers de particules ponctuelles, décrites par une action "skeleton" généralisant celle, géodésique, de la relativité générale. Enfin, à l’aide des "superpotentiels" de Katz, que l’on généralise pour définir la masse (nœtherienne) d’un trou noir à "cheveux" vectoriel et scalaire, on montre que la première loi de la thermodynamique qui en découle est particulièrement adaptée, lorsqu’un trou noir est membre d’un système binaire, pour en décrire les réajustements éventuels sous l’influence d’un compagnon lointain. La thermodynamique des trous noirs est alors utilisée pour interpréter et discuter du domaine de validité de leur "skeletonisation"
With the birth of "gravitational wave astronomy" comes the opportunity to test general relativity and its alternatives in a strong field regime that had never been observed so far: that of the coalescence of a compact binary sytem. This thesis studies the problem of motion and gravitational radiation from such systems in modified gravities, by adapting some of the key analytical tools that were first developed in the context of general relativity. First, we show how to widen the "effective-one-body" (EOB) formalism to a large class of modified gravities, including, e.g., scalar-tensor theories. In the latter, the gravitational interaction is described by supplementing general relativity with a (massless) scalar degree of freedom. The corresponding two-body lagrangian being known at post-post-keplerian order, we build an associated EOB hamiltonian, which describes the motion of a test particle orbiting in effective external fields. This enables to simplify and resum the two-body dynamics; and hence, to explore the strong-field regime near merger. We then "tackle", for the first time, the analytical description of "hairy" binary black hole systems, and obtain their (EOB) gravitational waveform counterparts in Einstein-Maxwell-dilaton theories, which generalize scalar-tensor theories by means of a (massless) vector field. To that end, we derive the two-body lagrangian at post-keplerian order as well as the energy flux radiated at infinity at quadrupolar order. As in general relativity, our developments rely on the phenomenological description of the black hole’s trajectories as worldlines of point particles that are, in turn, described by a "skeleton" action generalizing that of general relativity. Finally, we develop a formalism based on Katz’ "superpotentials" to define the mass (as a nœther charge) of a black hole that is endowed with vector and scalar "hair". We then deduce the first law of thermodynamics, which is particularly suitable to describe its readjustments when interacting with a faraway companion. Black hole thermodynamics is lastly shown to be a powerful tool to interpret and discuss the scope of their "skeletonization"

Thesis (Ph. D.) -- University of Maryland, College Park, 2006.
Thesis research directed by: Astronomy. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

This thesis investigates black holes and gravitational waves in the framework of quadratic gravity. These subjects are introduced by first examining the current state of general relativity and how it is realised. The discussion then addresses the quantitative aspects of black holes, gravitational waves, and quadratic gravity. This is then followed by the exploration of the three main research topics. The first research topic investigates the induced charging of a black hole due to a topological term in quadratic gravity. The second research topic focuses on the approximate analytic non-Schwarzschild black hole solutions in quadratic gravity. Finally, gravitational waves generated by binary systems within quadratic gravity are studied, with a focus on the corrections produced by the massive scalar field and the massive spin-2 field.

We consider a model of inflation, called Fibre Inflation, derived from string theory in the framework of type IIB flux compactification and we study the production of primordial black holes due to the gravitational collapse of the curvature perturbations. They are a good candidate for dark matter and if their mass was between 10^-17 and 10^-13 solar masses then their contribution to the total dark matter abundance would be between 10% and 100%. The inflaton potential has enough tuning freedom to allow for a flat plateau at large field values, corresponding to the usual slow roll behaviour, and an inflection point near the minimum that enhances the scalar perturbations. It is the latter feature that greatly increases the density anisotropies from the usual δρ/ρ ~ 10^-5, typical of the CMB radiation, to δρ/ρ ~ 10^-1 due to a peak in the primordial power spectrum that allows for the formation of black holes. The latter is computed solving the Mukhanov-Sasaki equation numerically using the Hubble slow roll parameters extracted from the solutions to the Friedmann equations and the inflaton equation of motion. The formation of black holes is followed by the production of a stochastic background of secondary gravitational waves: in this thesis we compute their amplitude and compare it with current observational bounds and the sensitivities of earth- and space-based interferometers. Our result is within reach of experiments like DECIGO and BBO, hence in the future it will be possible to have a comparison between our theoretical results and observations.

A number of scenarios have been proposed for the origin of the supermassive black holes (SMBHs) that are found in the centres of most galaxies. Many such scenarios predict a high-redshift population of massive black holes (MBHs), with masses in the range 10² to 10⁵ times that of the Sun. When the Laser Interferometer Space Antenna (LISA) is finally operational, it is likely that it will detect on the order of 100 of these MBH binaries as they merge. The differences between proposed population models produce appreciable effects in the portion of the population which is detectable by LISA, so it is likely that the LISA observations will allow us to place constraints on them. However, gravitational wave detectors such as LISA will not be able to detect all such mergers nor assign precise black hole parameters to the merger, due to weak gravitational wave signal strengths. This dissertation explores LISA's ability to distinguish between several MBH population models. In this way, we go beyond predicting a LISA observed population and consider the extent to which LISA observations could inform astrophysical modelers. The errors in LISA parameter estimation are applied in two ways, with an 'Error Kernel' that is marginalized over astrophysically uninteresting 'sample' parameters, and with a more direct method which generates random sample parameters for each source in a population realization. We consider how the distinguishability varies depending on the choice of source parameters (1 or 2 parameters chosen from masses, redshift or spins) used to characterize the model distributions, with confidence levels determined by 1 or 2-dimensional tests based on the Kolmogorov-Smirnov test.

Thesis (Ph. D.) -- University of Maryland, College Park, 2007.
Thesis research directed by: Physics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

This thesis presents theoretical results on the tidal disruption of stars by supermassive black holes (SMBHs). The multiwavelength ares produced by tidal disruption events (TDEs) have supernova-like luminosities, and associated relativistic jets can be visible to cosmological distances. TDEs probe the demography of quiescent SMBHs, and are natural laboratories for jet launching mechanisms and super-Eddington accretion. The first chapter broadly surveys TDE physics. The second and third chapters estimate the TDE rate following gravitational wave (GW) recoil of a SMBH (after a SMBH binary merger). Immediately after GW recoil, the TDE rate increases, sometimes to \(~10^{-1}\) TDEs per year. This "burst" of TDE flares can provide an electromagnetic counterpart to low frequency GW signals, localizing sources and measuring cosmological parameters. Millions of years later, recoiled SMBHs wandering through their host galaxies will produce spatially offset TDEs at a rate which is likely detectable with the LSST. In the fourth chapter, we show that standard estimates for \(\Delta\epsilon\), the energy spread of TDE debris, are wrong, sometimes by orders of magnitude. Correcting this error reduces the observability of many TDEs. We introduce a new analytic model for tidal disruption, calculate \(\Delta\epsilon\)'s dependence on stellar spin, estimate general relativistic corrections to \(\Delta\epsilon\), and quantify the GW signal generated from tidal compression. The fifth chapter presents hydrodynamical simulations of TDE debris circularization, focusing on eccentric, rather than parabolic, orbits. General relativistic precession drives debris circularization, in contrast to past simulations using smaller black holes. In the sixth chapter, we show that TDE light curves can constrain or measure SMBH spins, as Lense-Thirring torques produce quasiperiodic variability in disk emission. Precession of a relativistic jet could also measure SMBH spin, and we apply our model to the relativistic Swift 1644+57 TDE. The seventh chapter considers the disruption of neutron stars (NSs) by stellar mass black holes (BHs) or other NSs. Jet precession in associated short-hard gamma ray bursts is uniquely possible for NS-BH (not NS-NS) mergers. We quantify typical precession amplitudes and periods, and calculate their time evolution. If disk viscosities are relatively low, electromagnetic observations alone could distinguish NS-BH from NS-NS mergers.
Astronomy

We investigate several aspects of black hole physics. First, we consider models of gravity minimally coupled to scalar fields. We derive a new class of asymptotically flat black holes sourced by a non-trivial asymptotically massless scalar field; we discuss their relationship with known solutions and standard no-hair theorems and their thermodynamics. We derive exact neutral and charged brane solutions sourced by a scalar field with vanishing potential, which are conformal to the Lifshitz spacetime; we discuss the symmetries and their holographic application for hyperscaling violation; we also give a quite general classification of brane solutions sourced by scalar fields useful for holographic applications. We study an inflationary model inspired by the domain wall/cosmology correspondence in which inflation is driven by a scalar with a two-exponential potential; we derive its phenomenological consequences in the slow-roll approximation and compare its predictions with the Planck 2015 data. Second, we investigate ultra-compact astrophysical objects which can act as black hole mimickers, in particular boson stars and wormholes. We discuss the existence and the stability of boson stars in higher dimensions and boson stars built with multiple scalars. We compute tidal Love numbers for various mimickers and discuss how to distinguish black holes from their possible mimickers with gravitational-wave data. We study the gravitational radiation emitted by a particle falling into an exotic compact object and show that the initial ringdown signal cannot be use distinguish between a black hole and a black hole mimicker.
We investigate several aspects of black hole physics. First, we consider models of gravity minimally coupled to scalar fields. We derive a new class of asymptotically flat black holes sourced by a non-trivial asymptotically massless scalar field; we discuss their relationship with known solutions and standard no-hair theorems and their thermodynamics. We derive exact neutral and charged brane solutions sourced by a scalar field with vanishing potential, which are conformal to the Lifshitz spacetime; we discuss the symmetries and their holographic application for hyperscaling violation; we also give a quite general classification of brane solutions sourced by scalar fields useful for holographic applications. We study an inflationary model inspired by the domain wall/cosmology correspondence in which inflation is driven by a scalar with a two-exponential potential; we derive its phenomenological consequences in the slow-roll approximation and compare its predictions with the Planck 2015 data. Second, we investigate ultra-compact astrophysical objects which can act as black hole mimickers, in particular boson stars and wormholes. We discuss the existence and the stability of boson stars in higher dimensions and boson stars built with multiple scalars. We compute tidal Love numbers for various mimickers and discuss how to distinguish black holes from their possible mimickers with gravitational-wave data. We study the gravitational radiation emitted by a particle falling into an exotic compact object and show that the initial ringdown signal cannot be use distinguish between a black hole and a black hole mimicker.

According to Einstein's theory of General Relativity, the acceleration of matter can cause ripples in the curvature of spacetime, given the name gravitational waves. Such ripples are negligible in magnitude for all but the most energetic astrophysical events, such as the coalescence of compact binary stars. In 2015, gravitational waves were first directly detected from a binary black hole (BBH) coalescence [19]. This was achieved using two independent laser interferometers which each measured the fluctuations caused by the gravitational waves as they passed by. Matched filtering and other data analysis techniques were then employed to identify the properties of the source and measure the likelihood that the detection is a false alarm. The efficacy of these matched filtering techniques is pivotal to not only detecting gravitational waves, but drawing as much information about their sources as possible. The methods for detecting a BBH involve the construction of a template bank; a group of synthesised waveforms which each represent a detectable series of gravitational waves that a BBH could produce. The characteristics of a BBH template are governed by the two masses and how they spin, the distance to the source, its orientation and its sky location. Current template banks do not include templates for sources where the spins are misaligned with the orbital momentum, which is the cause of precession in BBH. Thus, the algorithms are effective for detecting a non-precessing BBH, but much less sensitive towards precessing sources. Creating a template bank which includes all possible precessing waveforms is computationally infeasible and would induce enough statistical noise to negate any extra sensitivity gained. However, many precessing signals would be undetectable or indistinguishable from non-precessing signals. Including such signals in a bank would result in no gain in its sensitivity. This thesis attempts to locate areas of precessing parameter space where waveforms are distinguishable from non-precessing sources, and begins work on forming a function which maps observable precession through parameter space.

This thesis is conceptually divided into two parts. The first and main part concerns the generation of gravitational radiation that is emitted from merging black-hole binary systems using Numerical Relativity methods. The second part presents the methodology of the search for gravitational-wave bursts that are emitted in core-collapse Supernovae. My approach to Numerical Relativity is to utilise the late-time gravitational radiation of merging binary black holes to extract key astrophysical parameters from such systems via standard parameter estimation techniques. I begin with an introductory chapter that outlines the standard theories of stationary and perturbed black holes. In addition, up-to-date techniques in performing binary black hole simulations, the current and near-future status of the global network of gravitational-wave detectors, as well as the most promising gravitational-wave sources. I conclude the chapter with elements on parameter estimation techniques, such as Bayesian analysis and the Fisher information matrix. In Chapter 2, I discuss detection issues and parameter estimation results from the late-time radiation of colliding non-spinning black holes in quasi-circular orbits, and propose a practical test of General Relativity, as well as of the nature of the merged compact object. Chapter 3 involves similar parameter extraction calculations, but involves a more realistic approach, whereby the effect of the various angular parameters on parameter estimation is considered, placing an emphasis on the actual science benefit from measuring the gravitational radiation from perturbed intermediate and supermassive black holes. In Chapter 4 we present the results of an extensive Numerical Relativity study of merging spinning black hole binaries and argue that the mass ratio and individual spins of a non-precessing progenitor binary can be measured solely by observing the late-time radiation. Chapter 5 presents the methodology in carrying out searches for gravitationalwave bursts (GWB) from core-collapse Supernovae with a dedicated for GWB searches pipeline (X-Pipeline) and presents the sensitivity performance of XPipeline in detecting GWBs associated with certain Supernova candidates during the two most recent LIGO-Virgo-GEO Science Runs.

The coalescence of two stellar mass black holes is regarded as one of the most promising sources for the first gravitational-wave (GW) detection with ground-based detectors. The current detection strategies, however, rely on theoretical knowledge of the gravitational waveforms. It is therefore crucial to obtain an accurate and complete description of the GW signal. This thesis concerns the description of precessing black holes. Misalignment between the orbital angular momentum and the spin angular momenta of the two black holes induces precession, leading to complex dynamics that leaves a direct imprint on the GW. Additionally, the evolution of the binary depends on the mass ratio and both spins spanning a sevendimensional intrinsic parameter space. This makes it difficult to obtain a simple, closed-form description of the waveform through inspiral, merger and ringdown. We are therefore interested in 1) developing a conceptually intuitive framework to systematically model precessing waveforms and 2) exploring the possibility of representing the seven-dimensional parameter space by a lower-dimensional subset. First, we introduce an accelerated frame of reference, which allows us to track the precession of the orbital plane. We then analyse the waveforms in this co-precessing frame resulting in an approximate decoupling between the inspiral and precession dynamics. This leads to the important identification of the inspiral rate of a precessing binary with the inspiral rate of an aligned-spin binary. Based on this decoupling, we develop a general framework to construct precessing waveforms by 'twisting up' an aligned-spin waveform with a model for the precession dynamics. In general, precession depends on all seven intrinsic physical parameters, which complicates modelling efforts. However, we find a parameter-reduced representation of the dynamics, which allows us to produce a first closed-form description of the complete waveforms of precessing black-hole binaries within this general and easy-to-grasp framework.

I buchi neri (BHs) sono oggetti variegati ed affascinanti in Natura. Il loro regno si estende dai buchi neri stellari con masse $sim 10-10^2 msun$ fino a BH supermassivi di $10^{9-10} msun$ al centro delle galassie. Mentre i primi sono il lascito dell'evoluzione stellare, i secondi sono il risultato di multipli merger di aloni di dark matter nella cosmologia $Lambda$CDM. Quando due BHs sono abbastanza vicini, formano una binaria (BHBs) ed emettono onde gravitazionali (GWs) che possiamo rilevare con i nostri interferometri. Come i BHs, anche le BHBs possono dividersi in diverse sottopopolazioni, ognuna con le proprie proprietà e caratteristiche: BHBs stellari (SBHBs) si formano dalla co-evoluzione di una binaria di stelle o in ambienti densi, mentre BHBs massicce (MBHBs) sono il risultato di merger di galassie. Le sfide nell'astronomia delle GW sono ancora numerose e richiedono varie conoscenze ed abilità per essere risolte. Per questa ragione, incomincio questa Tesi presentando dei risultati per SBHBs nei primi capitoli e virando verso MBHBs sul finale. Ogni capitolo ha la sua breve introduzione e discussione dei risultati. Nel capitolo 1 introduco alcuni concetti base della Relatività Generale (GR) legati all'emissione delle GWs. Riassumo lo stato corrente dell'astronomia delle GW. Spiego inoltre come GWs da BHBs possono essere modellizzate sotto alcune assunzioni ragionevoli e riporto alcune formule utili a capire i concetti dei paragrafi successivi. Nel capitolo 2 studio il minimo ordine Post-Newtonian (PN) necessario per seguire il segnale di SBHBs in LISA e realizzare una stima dei parametri corretta. Infatti gli SBHBs compiono numerosi cicli in LISA e quindi una descrizione accurata del segnale d'onda è necessaria per evitare bias nella stima dei parametri. Mostro come il fattore che determina il minimo ordine PN è il tempo alla coalescenza e che sistemi più vicini al merger richiedono più contributi PN. Applico questo risultato ad una popolazione di SBHBs in LISA per ottenere delle stime più realistiche, trovando che la maggior parte delle srogenti può essere descritta con correzzioni fino al 2PN, mentre i sistemi che mergono durante il tempo di missione richiedono contributi PN fino al 2.5PN o 3PN. L'argomento del capitolo 3 è un modello per descrivere BHs al di sopra del pair-instability mass gap, cioè BHs con massa $> 120 msun$. Presento un semplice modello e, sotto l'assuzione che la formazione della binaria non cambi oltre il gap, stimo il numero di eventi per i detector attuali, ET e LISA. Inoltre, suggerisco che le binarie non risolte possano formare un background casuale in LISA. Nel capitolo 4, mi muovo verso i MBHBs, osservabili solo dallo spazio con LISA. Introduco i concetti legati alla formazione ed evoluzione di MBHBs e le possibilità dell'astronomia multimessaggera. Descrivo anche come possiamo stimare i parametri della sorgente con il formalismo della Fisher matrix. Nle capitolo 5 presento un lavoro a cui ho contribuito sulla possibilità di osservare un modulazione Doppler in banda X durante l'inspiral di MBHBs. Prima del merger, emissione in banda X può essere prodotto dal gas che accresce sui BHs e il moto orbitale della binaria può imprimere una modulazione al segnale elettromagnetico in fase con il segnale di GWs. Osservare questa modulazione permetterebbe di determinare l'esatta posizione della sorgente nell'area di cielo stimata da LISA. Dalla nostra analisi, stimiamo di poter osservare qualche modulazione durante tutta la missione. Nel capitolo 6 riporto la stime dei parametri per MBHBs in funzione del tempo alla coalescenza. In particolare, mi concentro su posizione in cielo, distanza di luminosità, chirp mass e mass ratio e come i loro errori si riduciono mentre il sistema si avvicina al merger. A beneficio della community, rilascio i dati e delle formule analitiche per descrivere l'evoluzione di questi parametri. Discuto infine le prospettive multimessangere.
Black holes (BHs) are variegated and fascinating objects in Nature. Their realm extends from the stellar BHs with mass $sim 10-10^2 msun$ to the supermassive BHs of $10^{9-10} msun$ that reside in the center of galaxies. While the former are the expected outcome of stellar evolution, the latter are the results of multiple dark matter halo mergers in the standard $Lambda$CDM scenario. When two BHs are close enough, they form a binary BHs (BHBs) and emit gravitational waves (GWs) that we can detect with our inteferometers. Similarly to BHs, also BHBs can be divided into different sub-populations, each with its unique features and characteristics: stellar BHBs (SBHBs) form from the co-evolution of binary stars or in dense region, while massive BHBs (MBHBs) are the result of galaxy mergers. The challenges of GW astronomy are still numerous and require different knowledge and expertise to be solved. For this reason, I start this Thesis presenting result for SBHBs in the initial chapters and moving to MBHBs in the end. Each chapter has its own brief introduction and discussion of the main results and conclusions. In Chapter 1 I introduce some basic General Relativity (GR) concepts related to the emission of GWs. I summarise the current status of GW astronomy. I explain how GWs from BHBs can be easily modeled under some reasonable assumptions and report some formulas useful to understand the concepts of the following chapters. In Chapter 2 I study the minimum Post-Newtonian (PN) order necessary to accurately track SBHBs in LISA and perform an unbiased parameter estimation. SBHBs are expected to spend a large number of cycles in band, therefore an accurate waveform is necessary to avoid biases in the binary parameters. I show that the main factor affecting the PN accuracy is the time to coalescence with systems closer to merger requiring higher PN contributions. I apply the previous result to a realistic population of SBHBs in LISA in order to draw more realistic estimates: I find that most of the sources can be modeled with just 2PN corrections while systems merging during LISA time mission require up to 2.5PN and 3PN contributions. The topic of Chapter 3 is a model to describe SBHBs above the pair-instability mass gap, i.e. BHs with mass $> 120 msun$. I build a simple approach and, under the assumption that the binary formation does not change beyond the mass gap, I estimate the detected rate for current detectors, ET and LISA. Finally I also suggest the possibility that the undetected sources form a new source of stochastic background in LISA. In Chapter 4 I move to MBHBs, detectable only from space by LISA. I provide an introduction on MBHBs formation and evolution and the multimessenger possibilities. I also explain how we estimate source information with the so-called Fisher matrix formalism. In Chapter 5 I present a work I contributed where we explore the possibility to detect a Doppler modulated X-ray emission during the inspiral of MBHBs. In the last stage of merger, X-ray emission is expected as the result of gas accretion on each BHs and the orbital motion of the binary might imprint a Doppler modulation on the electromagnetic (EM) emission in phase with the GW signal. The detection of this modulation would allow to pinpoint the exact source location in the relatively large error area provided by LISA. From our analysis, we estimate few modulation detections over LISA time mission. Finally in Chapter 6 I report the results for the parameter estimation of MBHBs on the fly, i.e. as function of time before coalescence. In particular I focus on sky position, luminosity distance, chirp mass and mass ratio and how their errors decrease as the system approaches merger. For the benefit of the community, I release also the complete set of data and analytical fits to describe the time evolution in the aforementioned parameters. Finally I discuss the multimessenger prospects.

[cat] Aquesta tesi és un recull del treball realitzat en els darrers quatre anys d’investigació enfocats a la producció de simulacions de relativitat numèrica de forats negres binaris en configuracions genèriques, així com a l’anàlisi de les ones gravitacionals extretes de dites simulacions, les seves conseqüències pel models de formes d’ones gravitacionals existents i les seves implicacions per a la cerca i l’estimació dels paràmetres d’aquests sistemes en la natura. Per començar, he estudiat la prescripció de paràmetres inicials en les simulacions de relativitat numèrica. Un problema ben conegut a relativitat numèrica és la dificultat d’obtenir simulacions de forats negres en òrbites quasi-circulars, degut a imprecisions en la generació de les dades inicials que provoquen òrbites quasi-el líptiques amb una excentricitat residual. El primer projecte d’aquesta tesi ha estat el desenvolupament d’un procediment iteratiu, senzill i computacionalment eficaç per a la reducció de l’excentricitat a simulacions de relativitat numèrica de forats negres binaris, veure Cap. 4. Amb aquest mètode s’han generat formes d’ona gravitacionals quasi-circulars amb una excentricitat negligible, e O 􀀀��� 10􀀀���4 , que han estat utilitzades pel nostre grup per generar models quasi-circulars de formes d’ona gravitacionals. La flexibilitat del mètode anterior permet no tan sols reduir l’excentricitat de les simulacions numèriques, sinó també augmentar-la. Aquest fet ha permès la generació d’un banc de més de 60 simulacions de relativitat numèrica amb excentricitat moderada e 0:5. Aquest ha estat el segon projecte d’investigació de la tesi, veure Cap. 5. Amb aquest grup de simulacions s’han generat formes d’ona híbrides pel mode dominant (2; 2) entre les ones obtingudes per la teoria post-Newtoniana i les de relativitat numèrica. A més, s’ha estimat les limitacions dels models quasi-circulars actuals per estimar paràmetres d’aquestes fonts. Els resultats obtinguts demostren que els models quasi-circulars de formes d’ona que inclouen modes subdominants redueixen el biaix en alguns paràmetres com la distància i el ràtio de massa, respecte a models sense modes subdominants. Per altra banda, durant el doctorat també s’han estudiat les limitacions de dues aproximacions utilitzades habitualment per models d’ona quasi-circulars amb espins precessants, veure Cap. 6. Aquestes dues aproximacions s’han analitzat emprant únicament simulacions de relativitat numèrica incloent modes subdominants. Els resultats obtinguts confirmen el bon funcionament de les aproximacions pels modes dominants (2; 2), mentre que pel modes subdominants s’observa una degradació important degut a diferent causes depenent del mode estudiat, per exemple, els modes (2; 1) són molt sensibles a les asimetries entre modes que les aproximacions negligeixen, mentre que els modes (4; 3) i (3; 2) pateixen mescla de modes en la part del decaïment de l’ona que les aproximacions no tenen en compte. Finalment, s’ha analitzat la sensibilitat de dos algorismes de cerca emprats per les col laboracions LIGO i Virgo durant el segon període d’observació O2 per detectar senyals completes d’ones gravitacionals procedents de binàries de forats negres eccèntriques, veure Cap. 7. En aquest treball preliminar s’ha quantificat l’impacte de l’excentricitat sobre dos algorismes de cerca: un codi de filtrat adaptat basat en el coneixement de la morfologia de la senyal, i un codi de cerca sense modelat. En aquest estudi s’estima per primera vegada la sensibilitat d’ambdós algorismes injectant senyals excèntriques calculades a partir de simulacions de relativitat numèrica incloent espins alineats amb el moment angular orbital del sistema. Els resultats obtinguts mostren una major degradació de la sensibilitat de l’algorisme de filtrat adaptat a mesura que l’excentricitat augmenta, mentre que la sensibilitat de l’algorisme sense modelat no es veu quasi afectada per l’increment de l’excentricitat, i per tant, es pot identificar aquest darrer com una eina robusta per a la detecció de senyals excèntriques.
[spa] Esta tesis recoge el trabajo realizado en los últimos cuatro años de investigación enfocados en la producción de simulaciones de relatividad numérica de agujeros negros binarios en configuraciones genéricas, así como en el análisis de las ondas gravitacionales extraídas de dichas simulaciones, sus consecuencias para los modelos de formas de ondas existentes y sus implicaciones para la búsqueda y la estimación de los parámetros de dichos sistemas en la naturaleza. Para empezar, he estudiado la prescripción de parámetros iniciales en las simulaciones de relatividad numérica. Un problema bien conocido en relatividad numérica es la dificultad de obtener simulaciones de agujeros negros en órbitas casi-circulares, debido a imprecisiones en la generación de los datos iniciales que provocan órbitas casi-elípticas con una excentricidad residual. El primer proyecto de esta tesis ha sido el desarrollo de un procedimiento iterativo, sencillo y computacionalmente eficaz para la reducción de la excentricidad en simulaciones de relatividad numérica de agujeros negros binarios, ver Cap. 4. Con este método se han generado formas de onda gravitacionales casi-circulares con una excentricidad negligible, e O 􀀀�� 10􀀀��4 , que han sido usadas por nuestro grupo para generar modelos de formas de onda casi-circulares. La flexibilidad del método anterior permite no solo reducir la excentricidad de las simulaciones numéricas, sino también aumentarla. Este hecho ha permitido la generación de un banco de más de 60 simulaciones de relatividad numérica con excentricidad moderada e 0:5. Este ha sido el segundo proyecto de investigación de la tesis, ver Cap. 5. Con este grupo de simulaciones he generado formas de onda híbridas para el modo dominante (2; 2) entre las ondas obtenidas a partir de la teoría post- Newtoniana y las de relatividad numérica. Además, con colaboradores he estimado las limitaciones de los modelos casi-circulares actuales para estimar los parámetros de estas fuentes. Los resultados obtenidos demuestran que los modelos casi-circulares de formas de onda que incluyen modos subdominantes reducen el sesgo en algunos parámetros como la distancia y el ratio de masa, respecto a los modelos sin modos subdominantes. Por otro lado, durante el doctorado también se han estudiado las limitaciones de dos aproximaciones utilizadas comúnmente para modelos de onda casi-circulares con espines precesantes, ver Cap. 6. Estas dos aproximaciones se han analizado usando únicamente simulaciones de relatividad numérica incluyendo modos subdominantes. Los resultados obtenidos confirman el buen funcionamiento de las aproximaciones para los modos dominantes (2; 2), mientras que para los modos subdominantes se observa una degradación importante debido a diferentes causas dependiendo del modo estudiado, por ejemplo, los modos (2; 1) son muy sensibles a las asimetrías entre modos que las aproximaciones negligen, mientras que los modos (4; 3) y (3; 2) padecen mezcla de modos en la parte del decaimiento de la onda que las aproximaciones no tienen en cuenta. Finalmente, con colaboradores he analizado la sensibilidad de dos algoritmos de búsqueda, utilizados por las colaboraciones LIGO y Virgo durante el segundo período de observación O2, para detectar señales completas de ondas gravitacionales procedentes de binarias de agujeros negros excéntricos, ver Cap. 7. En este trabajo preliminar se ha cuantificado el impacto de la excentricidad sobre dos algoritmos de búsqueda: un código de filtrado adaptado y un código de búsqueda sin modelado. En este estudio se estima por primera vez la sensibilidad de ambos algoritmos inyectando señales excéntricas calculadas a partir de simulaciones de relatividad numérica. Los resultados muestran una mayor degradación de la sensibilidad del algoritmo de filtrado adaptado a medida que aumenta la excentricidad, mientras que el algoritmo sin modelado no se ve casi afectado por el aumento de la excentricidad, y por tanto, se puede identificar este último como una herramienta robusta para la detección robusta de señales excéntricas.
[eng] This thesis gathers all the work done in my last four years of research focused on the production of numerical relativity simulations of generic binary black holes, as well as the analysis of the gravitational waveforms from these simulations and their implications for searches and parameter estimation on those systems. I have started studying the prescription of initial parameters in numerical relativity simulations. A well known problem in numerical relativity is the difficulty to obtain simulations of black holes orbiting in quasi-circular orbits due to inaccuracies of the initial data, which cause elliptical orbits with residual eccentricity. The first project of the thesis has been the development of a simple, iterative and computationally efficient procedure to reduce the eccentricity in binary black hole numerical relativity simulations, see Chap. 4. With this method we have produced quasi-circular waveforms with negligible eccentricity, e O 􀀀� 10􀀀�4 , which have been used in our group to generate quasi-circular waveform models. The flexibility of the previous method permits not only the reduction of the eccentricity, but also increasing it. Using this fact I have produced a data set of more than 60 numerical relativity simulations with moderate eccentricity e 0:5. This has been the second project of the thesis, see Chap. 5. Taking this set of simulations, with collaborators I have generated hybrid waveforms for the dominant (2; 2) mode between post-Newtonian and numerical relativity waveforms. Moreover, we have estimated the limitations of the current quasi-circular waveform models to estimate the parameters from those sources. We have found that the quasi-circular models which include higher order modes reduce the bias in some parameters like the mass ratio and luminosity distance, with respect to those models not including higher order modes. Furthermore, during the Ph.D. I have also studied the limitations of two approximations commonly used by precessing quasi-circular waveform models, see Chap. 6. These two approximations have been analysed using exclusively numerical relativity simulations including higher order modes. The results confirm the good performance of the approximations for the (2; 2) modes, while one observes a clear degradation for higher order modes due to different reasons depending on the considered mode. For instance, the (2; 1) modes are found to be very sensitive to asymmetries which the approximations neglect, while the (4; 3) and (3; 2) modes, have mode-mixing in the ringdown part which is not properly taken into account by the simple approximations. Finally, with collaborators I have analysed the sensitivity of two search pipelines, used by the LIGO and Virgo collaborations during the O2 Science Run, to the full gravitational wave signal of eccentric binary black holes, see Chap. 7. In this preliminary work we have quantified the impact of eccentricity on two search pipelines: a matched-filter and an unmodeled search algorithm. We have for the first time estimated the sensitivity of both algorithms injecting eccentric signals computed from numerical relativity simulations. The results show a larger degradation of the sensitivity of the matched-filter algorithm with increasing eccentricity, while the sensitivity of the unmodeled search algorithm remains barely unaffected to the increase of eccentricity, thus, we consider the latter one a robust tool to detect such eccentric signals.

The present-day interest in gravitational waves, justified by the recent direct detections made by LIGO, is opening the exciting possibility to answer many questions regarding General Relativity in extreme situations. One of these questions is whether black hole are – indeed – described totally by their mass, charge and angular momentum or whether they can have additional long-range hair. This project is concerned with this question. We aim at studying the influence of additional structure on the black hole horizon in the form of long-range hair by studying linearized Einstein equation the solutions when perturbed. More precisely, we will study the Schwarzschild solution, pierced by an infinitely long and thin cosmic string such that the space-time possesses a global deficit angle. Quasi-normal modes are believed to dominate the gravitational wave emission during the ring down phase of an excited black hole that would e.g. be the result of a merger of two ultra-compact objects, therefore linearized perturbations can be considered. With the advent of gravitational wave astronomy the proposed study will be very important when reconstructing the source of the detected gravitational wave signals.
O atual interesse em ondas gravitacionais, justificado pelas detecções diretas feitas pela colaboração LIGO recentemente, está abrindo a excitante possibilidade de responder várias questões a respeito da Relatividade Geral em condições estremas. Uma dessas questões é se buracos negros são – realmente – totalmente discritos apenas por sua massa, carga e momento angular ou se eles podem ter os chamados cabelos de longo alcance adicionais. Nosso projeto se preocupa em responder esta pergunta. Nosso objetivo está em estudar a influência de uma estrutura adicional no horizonte de eventos de um buraco negro através do comportamento da equação linearizada de Einstein quando a solução é perturbada. Mais precisamente, nós estudaremos a solução de Schwarzschild atravessada por uma corda cósmica infinitamente fina, tal corda faz com que o espaço-tempo tenha um hiato angular em seu plano equatorial. Acredita-se que modos quasi-normais dominem a emissão de ondas gravitacionais durante a fase de ringing down de buracos negros excitados que podem, por exemplo, se originar da colisão de objetos ultra compactos, portanto perturbações lineares podem ser consideradas. Com o advento da astronomia através de ondas gravitacionais o estudo proposto será importante para que se possa reconstruir a origem de sinais detectados.

Astronomy with gravitational-wave observations is now a reality. Much of the theoretical research in this field falls under three broad themes: the mathematical description and physical understanding of gravitational radiation and its effects; the construction of accurate and computationally efficient waveform models for astrophysical sources; and the improved statistical analysis of noisy data from interferometric detectors, so as to extract and characterise source signals. The doctoral thesis presented in this dissertation is an investigation of various topics across these themes. Under the first theme, we examine the direct interaction between gravitational waves and electromagnetic fields in a self-contained theoretical study; this is done with a view to understanding the observational implications for highly energetic astrophysical events that radiate in both the gravitational and electromagnetic sectors. We then delve into the second theme of source modelling by developing and implementing an improved waveform model for the extreme-mass-ratio inspirals of stellar-mass compact objects into supermassive black holes, which are an important class of source for future space-based detectors such as the Laser Interferometer Space Antenna. Two separate topics are explored under the third theme of data analysis. We begin with the procedure of searching for gravitational-wave signals in detector data, and propose several combinatorial compression schemes for the large banks of waveform templates that are matched against putative signals, before studying the usefulness of these schemes for accelerating searches. After a gravitational-wave source is detected, the follow-up process is to measure its parameters in detail from the data; this is addressed as we apply the machine-learning technique of Gaussian process regression to gravitational-wave data analysis, and in particular to the formidable problem of parameter estimation for extreme-mass-ratio inspirals.

This thesis is a theoretical study of supermassive black holes (SMBHs) in merging galaxies. We consider the dynamics that govern inspiralling SMBH pairs and gravitational-wave (GW) recoiling SMBHs, as well as the fueling of active galactic nuclei (AGN) during galaxy mergers. In particular, we focus on the observable signatures that could distinguish dual or recoiling AGN from those in isolated galaxies, and we explore the implications of these events for the coordinated evolution of SMBHs and galaxies. In the second and third chapters, semi-analytical models for GW-recoiling SMBHs are developed. The second chapter illustrates that bound recoiling SMBHs may have long wandering timescales and that recoil events can self-regulate SMBH growth. In the third chapter, we study the evolution of recoiling SMBHs in evolving, gaseous merger remnants. We find that the presence of gas greatly influences recoiling SMBH trajectories and may partially suppress even large recoil kicks in some cases. We also show that kinematically- and spatially-offset AGN can have substantial lifetimes for a wide range in kick speeds. Finally, this chapter illustrates that GW recoil influences the observed SMBH-galaxy relations as well as central star formation in the merger remnant. In the fourth chapter we turn our attention to inspiralling SMBH pairs with kiloparsec-scale separations. We use a novel approach to model the narrow-line emission from these SMBH pairs, in order to understand their relationship to observations of double-peaked narrow-line AGN. Our results indicate that double-peaked narrow-line AGN often arise from gas kinematics rather than from dual SMBH motion, but that the latter are a generic, short-lived phase of SMBH inspiral in gaseous mergers. We identify several diagnostics that could aid in distinguishing the true AGN pairs in the double-peaked sample. Finally, the fifth chapter examines a particular galaxy that exhibits signatures of both a recoiling AGN and an AGN pair. Applying methods developed throughout this thesis, we design models for both scenarios that are well-matched to the available data. Currently, neither possibility can be excluded for this object, but our models constrain the most relevant parameters for etermining its nature and for the design of future observations.
Astronomy

La gravité d’Horava brise la symétrie de Lorentz avec l’introduction d’une foliation intrinsèque de l’espace-temps, définie par un champ scalaire, le khronon. Cette foliation privilégiée rend les solutions de trous noirs plus compliquées que celles de la relativité générale, due à l’apparition de nouveaux horizons: un horizon de matière pour les champs de matière; l’horizon de spin-0 pour les excitations scalaires du khronon, l’horizon de spin-2 pour les ondes gravitationnelles; finalement un horizon universel pour des modes instantanés apparaissant dans l’ultraviolet. On étudie des trous noirs en mouvement lent par rapport au référentiel privilégié. Ces solutions sont cruciales pour déterminer les susceptibilités des trous noirs et prédire leur émission d’ondes gravitationnelles, en particulier l’émission dipolaire des binaires de trous noirs. On trouve que pour des valeurs arbitraires des constantes de couplage, les trous noirs en mouvement lent souffrent de singularités de courbure à l’horizon universel. Des singularités à l’horizon de spin-0 sont aussi présentes mais peuvent être absorbées si l’on sacrifie les solutions plates à l’infini. Cependant, on a trouvé un sous-ensemble de l’espace de paramètres, de dimension un, où les trous noirs en mouvement lent sont partout réguliers et coincident avec ceux de la relativité générale. En particulier, ils n’émettent pas de radiation dipolaire. Remarquablement, ce sous-ensemble est favorisé par les contraintes récentes de l’événement GW170817 ainsi que les tests dans le système solaire
Horava gravity breaks Lorentz symmetry by introducing a preferred spacetime foliation, which is defined by a timelike dynamical scalar field, the khronon. The presence of this preferred foliation makes black hole solutions more complicated than in General Relativity, with the appearance of multiple distinct event horizons: a matter horizon for matter fields; a spin-0 horizon for the scalar excitations of the khronon; a spin-2 horizon for tensorial gravitational waves; and even a universal horizon for instantaneously propagating modes appearing in the ultraviolet. We study how black hole solutions in Horava gravity change when the black hole is allowed to move with low velocity relative to the preferred foliation. These slowly moving solutions are a crucial ingredient to compute black hole sensitivities and predict gravitational wave emission (and particularly dipolar radiation) from the inspiral of binary black hole systems. We find that for generic values of the theory's three dimensionless coupling constants, slowly moving black holes present curvature singularities at the universal horizon. Singularities at the spin-0 horizon also arise unless one waives the requirement of asymptotic flatness at spatial infinity. Nevertheless, we find that in a one-dimensional subset of the parameter space of the theory's coupling constants, slowly moving black holes are regular everywhere, even though they coincide with the general relativistic ones (thus implying in particular the absence of dipolar gravitational radiation). Remarkably, this subset of the parameter space essentially coincides with the one selected by the recent constraints from GW170817 and by solar system tests

Les trous noirs supermassifs résident dans les centres de la plupart des galaxies massives et on observe des corrélations entre leurs masses et les propriétés de leurs galaxies hôtes. De plus, on observe des trous noirs de plus d’un milliard de masses solaires quelques centaines de millions d’années seulement après le Big Bang. Ces trous noirs supermassifs présents dans l’univers jeune ne sont que le sommet de l’iceberg de l’ensemble de la population de trous noirs, mais ils mettent en question notre compréhension de la formation et de la croissance des premiers trous noirs. Notre nouvelle méthode améliorant le calcul de la densité de colonne de H2 donne des probabilités pour former des graines massives de trous noirs qui sont plus d’un ordre de grandeur plus élevées que prédit précédemment. Nous trouvons que CR7 pourrait être le premier candidat à héberger un tel trou noir formé par effondrement direct et nous démentons l’existence initialement revendiquée d’une population stellaire massive primordial dans CR7. Nous calculons la densité des taux de fusion des trous noirs binaires des premières étoiles et leurs taux de détection avec aLIGO. Notre modèle démontre que les détections des ondes gravitationnelles à venir au cours des prochaines décennies permettront d’imposer des contraintes plus strictes sur les propriétés des premières étoiles et donc sur les scénarios de formation des premiers trous noirs. Nous développons un modèle analytique en 2D de la rétroaction des noyaux actifs de galaxie pour démontrer qu’un profil de disque plus réaliste réduit la quantité de gaz qui est éjectée du halo par rapport aux modèles 1D existants. La rétroaction empêche l’accretion de gaz sur le trou noir central pendant seulement ∼1 million d’année environ, ce qui permet une accretion de gaz presque continue dans le plan du disque. Avec cette thèse, je contribue à une meilleure compréhension de la formation et la croissance des premiers trous noirs supermassifs
Supermassive black holes reside in the centres of most massive galaxies and we observe correlations between their mass and properties of the host galaxies. Besides this correlation between a galaxy and its central black hole (BH), we see BHs more massive than one billion solar masses already a few hundred million years after the Big Bang. These supermassive BHs at high redshift are just the tip of the iceberg of the entire BH population, but they challenge our understanding of the formation and growth of the first BHs. Our improved method to calculate H2 self-shielding yields probabilities to form massive seed BHs that are more than one order of magnitude higher, than previously expected. We find that CR7 might be the first candidate to host such a direct collapse BH and we disprove the initially claimed existence of a massive metal-free stellar population in CR7. We calculate the merger rate density of binary BHs from the first stars and their detection rates with aLIGO. Our model demonstrates that upcoming detections of gravitational waves in the next decades will allow to put tighter constraints on the properties of the first stars and therefore on formation scenarios of the first BHs. We develop a 2D analytical model of active galactic nuclei-driven outflows to demonstrate that a more realistic disc profile reduces the amount of gas that is ejected out of the halo, compared to existing 1D models. The outflow prevents gas accretion on to the central BH for only about ∼1Myr, which permits almost continuous gas inflow in the disc plane. With this thesis, I contribute to a better understanding of the formation and growth of the first supermassive BHs

We employ the formalism of the Horizon Quantum Mechanics to describe the gravitational radius of compact sources by means of an operator and derive a Horizon Wave Function which will allow us to estimate the probability of formation of black holes in scattering processes. If the Planck scale is kept at its standard value, however, it will be impossible to test that regime with any foreseeable technology. We then review how the introduction of extra dimensions can potentially lower the Planck scale down to the TeV range in an attempt to solve the hierarchy problem. In this context, we proceed by studying black holes described by a generalisation of the Kerr metric for higher dimensional spacetime known as the Myers-Perry metric. Our computation of the probability that a rotating source in higher dimensions is a black hole suggests that, even if the fundamental Planck scale is as low as a few TeV's, we should not be able to detect any black hole in colliders as is indeed the case.

The standard cosmological model, ΛCDM, with the addition of an early inflationary phase, provides an accurate description of a nearly flat and homogeneous Universe, at large scales, which expands at an accelerated rate. Despite its vindication, our knowledge of the components that trigger the early formation of structures and drive the accelerated expansion of the Universe, that is, dark matter (DM) and dark energy respectively, is severely limited, given their feeble interactions with the other components of the Universe. A number of candidates from particle physics, e.g weakly interacting massive particles (WIMPs) or axions, have been proposed to constitute DM, but so far there has been no evidence to support their existence. However, the detection of a signal from the merger of a binary of black holes of stellar masses, reinvigorated the interest in an old candidate for DM, namely primordial black holes (PBHs). These black holes behave as the ones sitting at the end of stellar evolution, with the distinctive differences that they may form in significant fractions even well before the appearance of the first stars, with masses that may range from the Planck mass, to the order of MBH ∼ 1012 M. One possible formation mechanism involves perturbations originating from the fluctuations of a scalar field during inflation, that collapse after they re-enter the causal horizon in a radiation or matter domination era. The PBHs could easily form binaries in the early Universe and merge within our Hubble time, rendering them observable by the current detectors LIGO/VIRGO. The work presented in this thesis focuses on how such a population of PBHs could be utilised in order to elucidate certain spectral features of curvature perturbations characterizing the initial state of the Universe. Firstly, the effect of matter and radiation perturbations on the orbital parameter distributions of PBH binaries is studied. These perturbations are shown to provide a source of torque to the binary, particularly when their power spectrum is enhanced at the comoving scale of the binaries, leading to the suppression of the merger rate and subsequent relaxation of constraints on the PBH abundance. Secondly, the effect of primordial clustering on the distribution of orbital parameters of PBH binaries is investigated with the use of a phenomenological model of local non-Gaussianity. It is shown that due to the modal coupling of the perturbations, the merger rate and the stochastic background of gravitational waves (SBGW) sourced by merging PBH binaries, are altered. An immediate result of clustering is that the observational constraint on the abundance of PBHs in DM is relaxed considerably, allowing for significant fractions, even close to totality. Thirdly, the possibility that the SBGW from the mergers of massive PBHs could provide an explanation for the recently detected isotropic signal by the NANOGrav collaboration is considered. The presence of non-Gaussianity, sourced from a phase of constant roll, is essential in order for such massive PBHs to evade the CMB µ-distortions constraints, in which case they may have formed in small abundances, of order 0.1% with respect to DM. The present work aims to provide a more robust modelling of the observational consequences of a population of PBHs in order to gain more insight into the spectrum of primordial perturbations at small scales and therefore into the initial conditions of the early Universe.
El modelo cosmológico estándar, ΛCDM, con una temprana fase de inflación, nos proporciona una descripción precisa de un Universo casi plano y homogéneo a gran escala, que se expande a un ritmo acelerado. A pesar de las evidencias observacionales, nuestro conocimiento del 95% de la energía del Universo, es decir, la materia oscura (DM) y la energía oscura, está limitado por la falta de una detección directa, debido en parte a la poca interacción, aparte de la gravitacional, que tienen con el resto de la materia. La detección de la primera señal de un sistema binario de agujeros negros, revitalizó el interés por un viejo candidato a materia oscura, los agujeros negros primordiales (PBHs). Los PBHs han recibido atención dado que se pueden formar con abundancias importantes durante el Universo temprano y con una amplia gama de posibles masas. Esta tesis se centra en su empleo para explorar el espectro de potencias de las perturbaciones de curvatura a escala pequeña. Primero, se estudia el efecto de las perturbaciones cosmológicas sobre los parámetros orbitales de los sistemas binarios de PBHs. Cuando hay una meseta de amplitud considerable en el espectro de potencia en las escalas de los sistemas binarios, la tasa de fusión se ve afectada, relajando los limites de la abundancia de PBHs. Segundo, se muestra que debido al acoplamiento modal de las perturbaciones, introducido por la presencia de no-Gaussianidad, se alteran la tasa de fusión y el resultante fondo estocástico de las ondas gravitacionales (SBGW) y que esto tambien resulta en la relajación de las restricciones de la abundancia de PBH. Tercero, se considera la posibilidad de que el SBGW proveniente de los sistemas binarios de PBHs super masivos pueda proporcionar una explicación para la señal detectada por NANOGrav. La presencia de no-Gaussianidad es esencial para que estos PBHs masivos eviten las µ-distorsiones de la CMB y se puedan haberse formado en abundancias del orden ∼ 0, 1%. Los PBHs constituyen una sonda única para explorar las condiciones iniciales del Universo y este trabajo pretende aportar un modelaje más robusto de las consecuencias observacionales de una población de PBHs.

The first part of this thesis is concerned with the question of global uniqueness of solutions to the initial value problem in general relativity. In 1969, Choquet-Bruhat and Geroch proved, that in the class of globally hyperbolic Cauchy developments, there is a unique maximal Cauchy development. The original proof, however, has the peculiar feature that it appeals to Zorn’s lemma in order to guarantee the existence of this maximal development; in particular, the proof is not constructive. In the first part of this thesis we give a proof of the above mentioned theorem that avoids the use of Zorn’s lemma. The second part of this thesis investigates the behaviour of so-called Gaussian beam solutions of the wave equation - highly oscillatory and localised solutions which travel, for some time, along null geodesics. The main result of this part of the thesis is a characterisation of the temporal behaviour of the energy of such Gaussian beams in terms of the underlying null geodesic. We conclude by giving applications of this result to black hole spacetimes. Recalling that the wave equation can be considered a “poor man’s” linearisation of the Einstein equations, these applications are of interest for a better understanding of the black hole stability conjecture, which states that the exterior of our explicit black hole solutions is stable to small perturbations, while the interior is expected to be unstable. The last part of the thesis is concerned with the wave equation in the interior of a black hole. In particular, we show that under certain conditions on the black hole parameters, waves that are compactly supported on the event horizon, have finite energy near the Cauchy horizon. This result is again motivated by the investigation of the conjectured instability of the interior of our explicit black hole solutions.

Orientador: Prof. Dr. Roldão da Rocha Jr.
Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2017.
Neste trabalho foram investigadas algumas conseguências da física de buracos negros em teorias cujo domínio está além do domínio da relatividade geral, em especial em teorias efetivos com dimensões extras. A investigação foi em substancialmente conduzida baseando-se em três efeitos gravitacionais, a saber, a radiação Hawking, o regime de deflexão forte de lentes gravitacionais e a formação de buracos negros quânticos. Uma solução de modelo cosmológico imerso em uma brana espessa foi também investigada. Modelos e teorias efetivas fornecem meios para testar os limites de validade de teorias conhecidas e indicam o que deveríamos esperar além desses limites. Baseado nessa ideia foram usados alguns modelos efetivos para estudar efeitos não previstos pela relatividade geral, associados a cada um dos fenômenos mencionados.
This work is devoted to investigate some consequences of black holes physics beyond the domain of general relativity, mainly in effective extra dimensional models. The investigation is carried along three gravitational effects, namely the Hawking radiation, the strong deflection of gravitational lensing and the formation of quantum black holes. A cosmological thick brane solution is also investigated. Effective theories and models provide a prominent approach for testing the limits of known theories and show what would be expected beyond that. Based on such idea we have used effective models for finding deviations of general relativity associated to each of the mentioned phenomena.

In physics, it is common to find different phenomena being described by similar equations. A good analogy can make us look at a problem from a different point of view. In that way, ideas may be transferred from one field of science to another, allowing to model new phenomena after previous, well-studied ones. In the case of the field of analogue gravity, systems that mimic certain aspects of the physics of curved spacetimes are studied. In this thesis, we are interested in the analogy between geometry and media. It has been known for several decades that light propagation in a gravitational field is formally equivalent to that in a bianisotropic medium. On the one hand, ray paths are bent due to spacetime curvature. On the other hand, spatial variations of the permittivity and permeability of a material can make light follow curved trajectories. These two phenomena can be related mathematically in the context of transformation optics, which provides the tools to determine the medium parameters necessary to mimic a certain coordinate transformation. Materials with these specific properties are not naturally occurring, therefore, the emergence of metamaterial science at the beginning of the century was needed to realize them. Metamaterials are artificial composite materials with sub-wavelength constitutive elements that exhibit exotic properties. They have been one of the hot topics of the past years given the variety of opportunities they offer: negative refraction, superlenses, indefinite dispersion, invisibility, among many others. In this thesis we study the analogues of two static spacetimes from the point of view of transformation optics: one with spherical symmetry and one with conical geometry. Both cases are inspired by solutions to Einstein’s equations: the Schwarzschild black hole and the cosmic string, respectively. For each case, we derive the permittivity and permeability of the analogous material using Plebanski’s formulation of the electromagnetic constitutive equations. We solve numerically the wave equation in the metamaterial and compare the results with analytical theories. We find that the spherically symmetric spacetime can be mimicked by either an anisotropic or isotropic medium due to its rotational symmetries. This is achieved by performing a coordinate transformation of the general metric to a conformally flat form. We obtain the medium parameters for both cases and apply the results to the case of the Schwarzschild black hole. We simulate the propagation of a Gaussian beam in the two materials and compare the numerical results with the null-geodesics in the Schwarzschild spacetime, finding a good agreement. The cosmic string is an example of a topological defect with conical geometry. A conical space can be interpreted as flat space with a wedge removed. We make use of this transformation to study the wave equation in the cosmic string background. We apply asymptotic diffraction theories to obtain analytical models that describe wave propagation of electromagnetic or gravitational waves (in a certain gauge). We find that our expressions reproduce accurately the results of the numerical simulations in the analogous metamaterial. Moreover, with our models, we can understand the observed diffraction pattern as the interference of four characteristic waves. With this interpretation we can introduce the Fresnel observation zones, which are related to the diffraction maxima. They help localize the regions – in either space or frequency – where the wave effects are more significant. In fact, in the diffraction by a non-compact object such as the cosmic string, we find that the contribution to the field of wave effects such as interference or diffraction can be of the same order as the geometrical optics terms. Furthermore, the conical topology also appears in condensed matter systems as disclinations or wedge dislocations, therefore we expect our results to be applicable in those systems as well.
La investigación en gravitación análoga consiste en el estudio de sistemas físicos donde se pueden reproducir algunos de los fenómenos propios de relatividad general. Esta tesis se centra en la conocida propagación análoga de las ondas electromagnéticas en un espacio-tiempo curvado y en un medio con una permitividad y permeabilidad generalmente anisótropas. Para la realización de este tipo de medios, fue necesaria la aparición de los metamateriales, materiales artificiales diseñados para tener propiedades electromagnéticas fuera de lo común. En este contexto, se estudian modelos análogos a dos objetos estáticos con distinta simetría: uno con simetría esférica y otro con topología cónica. Ambos casos están motivados por soluciones a las ecuaciones de Einstein: el agujero negro de Schwarzschild y la cuerda cósmica, respectivamente. A través de las ecuaciones de óptica de transformación, determinamos los parámetros de los medios análogos a estos espacio-tiempos. Estudiamos la propagación de ondas electromagnéticas en los materiales obtenidos mediante simulaciones numéricas y comparamos los resultados con teorías analíticas, encontrando muy buen acuerdo. Por un lado, los contrastamos con las geodésicas en los espacio-tiempos considerados a través del formalismo Hamiltoniano. Por otro lado, desarrollamos modelos analíticos para describir la difracción de una onda (en principio tanto electromagnética como gravitatoria) debido a la cuerda cósmica. Para ello, usamos teorías asintóticas de difracción en un espacio virtual plano con un déficit de ángulo, ya que es una representación equivalente a la geometría cónica de la cuerda. De este modo, se obtienen expresiones que nos permiten explicar detalladamente los fenómenos ondulatorios de interferencia y difracción que se producen en este espacio-tiempo. Observamos que estos efectos pueden ser comparables a los términos de óptica geométrica: añaden una modulación en la amplificación del campo relacionada con la formación de imágenes dobles propia de la topología de la cuerda. Cabe destacar que estos fenómenos son conceptualmente distintos a los que se podrían esperar en la difracción sobre un objeto sólido como una barra. Utilizando nuestros modelos analíticos, obtenemos el patrón de difracción característico de la cuerda cósmica, que podría ser de interés para su detección.