Dissertations / Theses on the topic 'Black hole structure'

We study a free quantum scalar field in the BTZ spacetime as a model of the AdS/CFT correspondence for black holes, and show the essential steps in computing Bogolyubov coefficients between modes on either side of the wormhole. As background, we review the BTZ geometry in standard, Kruskal and Poincaré coordinates, holographic renormalisation of the dual field theory and canonical quantisation in curved spacetime.
Vi studerar ett fritt skalärt kvantfält i BTZ-rumtiden som en modell av AdS/CFT-dualiteten för svarta hål och visar huvudstegen i beräkningen av Bogolyubov-koefficienter mellan moder på olika sidor av maskhålet. Som bakgrund redogör vi för BTZ-geometrin i standard-, Kruskal- och Poincarékoordinater, holografisk renormering av den duala fältteorin och kanonisk kvantisering i krökt rumtid.

Active galactic nuclei (AGN) are known to vary in brightness in all regions of the electromagnetic spectrum and over a wide range of timescales. Many methods have been utilized to transform this observed variability into meaningful information about the central engines of AGN. One such technique, adapted from time series analysis of galactic x-ray binary systems, has been used to detect a characteristic break timescale in the power density spectra of x-ray variability in Seyfert galaxies. This timescale, thought to be related to instabilities in the accretion disk, appears to scale with black hole mass over many orders of magnitude. This dissertation performs similar time series analyses with the optical data of eight blazars. The majority of these objects also display a characteristic break timescale. In cases where a black hole estimate is known, the timescales are in good agreement with the relationship observed for galactic x-ray binary systems and Seyfert galaxies. For objects of unknown mass, this relationship can be used to provide a mass estimate of the supermassive black hole. Comparisons are made between the structure function and power density spectrum for each object, and the implications for the connection between the accretion disk and the relativistic jet in AGN are discussed.

L’oggetto di tale tesi é lo studio di sistemi gassosi in rotazione assisimmetrica con distribuzioni barocline. Nella prima parte dell’elaborato, vengono discussi i concetti fondamentali della dinamica dei fluidi; le equazioni del moto di fluidi in rotazione soggetti ad un potenziale gravitazionale vengono derivate e studiate. Successivamente viene introdotta l’analisi sulla stabilità lineare e vengono derivati i criteri di Schwarzschild e di Rayleigh. Tali criteri vengono poi generalizzati introducendo il criterio di Solberg-Hoiland. Soluzioni stazionarie per fluidi in rotazione assisimmetrica vengono introdotte e vengono discusse le differenze nei casi barotropico e baroclino. Viene poi presentata una famiglia di sistemi baroclini in equilibrio in un potenziale gravitazionale assisimmetrico. Successivamente ho considerato una famiglia di tori gassosi con una distribuzione di densità a legge di potenza. Sono stati studiati due casi: tori auto-gravitanti e tori in equilibrio in presenza della loro auto-gravità e di un buco nero centrale. Infine, il criterio di Solberg-Hoiland é stato utilizzato per determinare in quali condizioni i sistemi toroidali auto-gravitanti sono linearmente stabili e per ottenere una formulazione analitica della condizione di stabilità per tori in equilibrio in presenza della loro auto-gravità e di un buco nero centrale.

This paper seeks to examine the failures of the current retirement plan structure, focusing on the structure’s reliance on unpredictable future market returns and the unwillingness of the parties involved to negotiate in order to further enhance their own self-centered interests. Currently, both defined contribution and defined benefit plans encounter a funding crisis in both the public and the private sectors. This paper will discuss how retirement plans, by nature, rely on assumptions of market returns, which naturally depend on the volatility of the market and increase the risk and uncertainty in retirement plans. In addition, since defined benefit plans mostly exist in the public sector today, this paper will examine defined benefit plans in relation to the public sector’s funding crisis and hope to shed light on the politics and tensions between the parties involved in public retirement plans that are preventing effectiveness and efficiency. Finally, this paper will also present alternative retirement plan strategies for which academics and scholars have advocated. However, at the end of the day, as opposed to relying on others to dictate one’s future benefits, which are based on the goodwill of others and uncertainty in the market, Americans should recognize their lack of savings and improve their personal financial literacy and develop individualized savings plans.

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

Le Centre de notre Galaxie est l'endroit idéal pour observer les effets de fort champ gravitationnel. Bien que l'on suppose généralement que la source radio compacte située en son centre et appelée Sgr A* soit un trou noir en rotation, des modèles alternatifs permettent d'expliquer les observations actuelles. Ce travail considère un de ces autres objects possibles : l'étoile bosonique. Les étoiles bosoniques en rotation sont des solutions numériques du système déquations couplées Einstein-Klein-Gordon, donc ces équations sont ici écrites sous forme 3+1 et un code numérique capable de les résoudre est présenté grâce à la bibliothèque Kadath. Plusieurs types d'étoiles bosoniques sont présentées avec différents potentiels tels que les champs libres, les champs auto-interagissants, des potentiels quartiques et sextiques, et différentes valeurs du nombre rotationnel quantique. Ensuite deux méthodes différentes de comparaison de ces espace-temps à celui de Kerr sont présentés. Le premier consiste à tracer les géodésiques de genre temps dans cette géométrie et à les étudier. Le code de ray-tracing appelé Gyoto a été utilisé pour intérger numériquement les équations géodésiques pour différents types d'étoiles bosoniques. Un type d'orbites particulier a été identifié : celles dont le moment angulaire est nul, elles ont été appelées orbites en "pétales pointus" à cause de leur forme. Ces orbites passent très près du centr et sont qualitativement différentes des orbites autour d'un trou noir de Kerr. Un autre moyen de comparer Kerr à un espace-temps stationnaire, asymptotiquement plat donné sous forme 3+1 est d'utiliser une caractérisation de l'espace-temps de Kerr donnée par le tenseur de Simon-Mars. Ce tenseur a la propriété d'être identiquement nul pour un espace-temps vide et asymptotiquement plat si et seulement si cet espace-temps est localement isométrique à celui de Kerr. L'idée est donc de construire une quantité scalaire, qui est un facteur de qualité invariant, de l'écrire sous forme 3+1 pour pouvoir le calculer grâce à des codes numériques. Calculer cette quantité permet d'obtenir une manière simple de comparer localement n'importe quel espace-temps stationnaire (même non vide et non analytique) à l'espace-temps de Kerr, cela donnant une mesure de sa déviation à Kerr. Comme illustration, ce facteur de qualité invariant est évalué pour des solutions numériques des équations d'Einstein générées par des étoiles bosoniques et des étoiles à neutrons, et pour des solutions analytiques de ces équations telles que l'espace-temps de Curzon-Chazy
The Galactic Center is an interesting place to test possible effects of strong gravity regime. Whereas it is generally believed that the compact object located at the Galactic Center, named Sgr A*, is a rotating black hole, some alternative models can also explain the current observations. This work is centered on one of these other objects, which is the Boson Star. Rotating boson stars are numerical solutions of the coupled Einstein-Klein-Gordon system, so these equations are written within the 3+1 formalism and then a numerical code capable of solving them with the Kadath library has been developed. Several kinds of boson stars with different potentials are presented : free fields an self-interacting fields, with quartic and sextic potentials, and different values of the rotational quantum number. Then two different ways of comparing this spacetime to Kerr's are presented. One way was to compute timelike geodesics in this geometry and study them. For that the ray-tracing code Gyoto is used to integrate numerically the geodesic equations for several types of boson stars. A peculiar type of orbits has been identifyed: the zero-angular-momentum ones which is called pointy-petal orbits thanks to their shape. These orbits pass very close to the center and are qualitatively different from orbits around a Kerr black hole. Another way to compare Kerr to any stationary and asymptotically flat metric given in its 3+1 form was to us a the characterization of the Kerr spacetime given by the Simon-Mars tensor. This tensor has the property of being identically zero for a vacuum and asymptotically flat spacetime if and only if the latter is locally isometric to the Kerr spacetime. The idea was to build a scalar with this tensor, and a scalar which is an invariant quality factor. Then, write it in 3+1 form to be able to compute it with numerical codes such as Kadath. Computing this scalar provides a simple way of comparing locally a generic (even non vacuum and non analytic) stationary spacetime to Kerr, therefore measure its 'non-Kerness". As an illustration, this invariant quality factor is evaluated for numerical solutions of the Einstein equations generated by boson stars and neutron stars, and for analytic solutions of the Einstein equations such as Curzon Chazy spacetime

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.

Over a century since its inception, general relativity continues to lie at the heart of some of the most researched topics in theoretical physics. It seems likely that the coveted solutions to problems like quantum gravity are to be found in an extension of general relativity, one which may only be visible in an alternate formulation of the theory.  In this thesis we consider the possibility of casting general relativity in the form of an initial value problem where spacetime is seen as the evolution of space. This evolution is shown to be constrained and of Hamiltonian type.  Not all spacetimes are physically acceptable. To be compatible with particle physics, one would like spacetime to accommodate fermions. Here we can take comfort in Geroch’s theorem, which implies that any spacetime that admits a Hamiltonian formulation automatically supports the existence of fermions. We review the elements that go into the proof of this theorem.
Allmän relativitetsteori har i över hundra år legat i teoretiska fysikens framkant. Det är möjligt att lösningarna på öppna problem som kvantiseringen av gravitation går att finna i en utvidgning av allmän relativitetsteori – och kanske uppenbarar sig denna utvidgning bara ur en alternativ formulering av teorin. I den här uppsatsen formuleras allmän relativitetsteori och dess Einsteinekvationer som ett begynnelsevärdesproblem, genom vilket rumtiden kan betraktas som rummets historia. Vi visar att rummets rörelseekvationer är Hamiltons ekvationer med tvångsvillkor.  Enligt partikelfysiken bör fermioner kunna finnas till i rumtiden. Härom kan vi åberopa Gerochs sats, enligt vilken rumtider som har en Hamiltonsk formulering också medger fermioner. Vi redogör för huvuddragen i beviset av Gerochs sats.

Els forats negres acústics en mecànica (coneguts per les sigles ABHs, de l’anglès Acoustic Black Holes) solen estar formats per osques en bigues i plaques, el gruix de les quals decau segons una llei potencial. L’efecte de l’ABH és el d’alentir les velocitats de fase i de grup de les ones de flexió incidents de tal manera que, en teoria, faria falta un temps infinit perquè les ones arribessin al centre de l’ABH, si el gruix d’aquest últim fos exactament zero. Tanmateix, a la pràctica això no és possible tot i que es pot aconseguir una forta dissipació col·locant una capa de material esmorteïdor al centre de l’ABH, on es concentra la major part de l’energia de les ones. En els darrers anys, els ABHs no només s’han explotat com a mètode passiu per reduir vibracions estructurals i l’emissió corresponent de soroll, sinó que també s’ha explorat el seu potencial per altres aplicacions com la manipulació d’ones o la captació d’energia. Aquesta tesi té tres objectius principals. Així, doncs, després d'una introducció general als ABHs, el treball s’ha dividit en tres grans seccions. La primera aborda aplicacions dels ABHs en bigues rectes i plaques planes. Per començar, es proposa i s’analitza un voladís piezoelèctric amb un acabament d’ABH per capturar energia. A continuació es presenten ABHs en forma d’anell per tal d’aïllar punts d’excitació externs en plaques planes i així evitar la transmissió de vibracions. Finalment, es contemplen configuracions periòdiques de matrius d’ABHs per tal de col·limar feixos d'ones de flexió i concentrar la seva energia en zones predeterminades d’una placa. La segona part de la tesi proposa nous dissenys d’ABHs per a estructures amb curvatura. Aquestes són molt habituals en els sectors naval, aeronàutic i industrial, de manera que val la pena investigar si els ABH poden resultar alguns casos. La secció comença analitzant la inclusió d’ABHs en bigues circulars i es veu com això dona peu a l’aparició de fenòmens típics en sistemes periòdics. Acte seguit es proposa un ABH anular per reduir les vibracions en conductes cilíndrics. En concret, es tracten els casos d’un conducte simplement suportat amb un ABH anular, i el d’un conducte amb ABH, suports periòdics i rigidificadors. Per finalitzar la secció, s’investiguen els efectes dels ABH anulars en la radiació acústica del conducte tenint en compte el nivell de potència acústica, l’eficiència de radiació i la intensitat supersònica. La tercera part de la tesi és més curta que les anteriors i simula l’aïllament d'una placa amb múltiples ABHs, en el rang de mitja i alta freqüència. A tal efecte s’empra el mètode de l’anàlisi estadística de distribució modal d'energia (SmEdA: statistical modal energy distribution analysis). En aquesta secció, l’estructura amb ABHs ja no s’analitza com un element individual sinó que s’acobla a dues cavitats d’aire, formant part d’un sistema mecànic més complex. Al llarg de la tesi s’utilitza repetidament el mètode d’expansió gaussiana (GEM: Gaussian expansion method). Pel GEM entenem prendre funcions gaussianes com a base per resoldre equacions diferencials en derivades parcials en el marc del mètode de Rayleigh-Ritz. El GEM s’assembla molt als enfocaments d’ondetes, però ofereix alguns avantatges en el cas de condicions de contorn periòdiques. Al principi de la tesi s’exposa un breu repàs del GEM i, quan és necessari, s’aborda la seva reformulació per a un problema particular en el capítol corresponent.
Los agujeros negros acústicos en mecánica (conocidos por las siglas ABHs, del inglés Acoustic Black Holes) suelen estar formados por muescas en vigas y placas, el grueso de las cuales decae según una ley potencial. El efecto del ABH es el de ralentizar las velocidades de fase y de grupo de las ondas de flexión incidentes de tal modo que, en teoría, haría falta un tiempo infinito para que las ondas alcanzaran el centro del ABH, si el grueso de este último fuera exactamente cero. Sin embargo, en la práctica esto no es posible, aunque se puede conseguir una fuerte disipación colocando una capa de material amortiguador en el centro del ABH, donde se concentra la mayor parte de la energía de las ondas. En los últimos años, los ABHs no sólo se han explotado como método pasivo para reducir vibraciones estructurales y la consecuente emisión de ruido, sino que también se ha explorado su potencial para otras aplicaciones como la manipulación de ondas o la captación de energía. Esta tesis tiene tres objetivos principales. Así pues, tras una introducción general a los ABHs, el trabajo se ha dividido en tres grandes secciones. La primera aborda aplicaciones de los ABHs en vigas rectas y placas planas. Para empezar, se propone y analiza un voladizo piezoeléctrico con un acabado de ABH para capturar energía. A continuación, se presentan ABHs en forma de anillo para aislar puntos de excitación externos en placas planas y así evitar la transmisión de vibraciones. Finalmente, se contemplan configuraciones periódicas de matrices de ABHs para colimar haces de ondas de flexión y concentrar su energía en zonas predeterminadas de una placa. La segunda parte de la tesis propone nuevos diseños de ABHs para estructuras con curvatura. Estas son muy habituales en los sectores naval, aeronáutico e industrial, por lo que merece la pena investigar si los ABH pueden dar buenos resultados en algunos casos. La sección comienza analizando la inclusión de ABHs en vigas circulares y se ve como estos dan pie a la aparición de fenómenos típicos de sistemas periódicos. Seguidamente se propone un ABH anular para reducir las vibraciones en conductos cilíndricos. En concreto, se tratan los casos de un conducto simplemente soportado con un ABH anular, y el de un conducto con ABH, soportes periódicos y rigidificadores. Para finalizar la sección, se investigan los efectos de los ABH anulares en la radiación acústica del conducto teniendo en cuenta el nivel de potencia acústica, la eficiencia de radiación y la intensidad supersónica. La tercera parte de la tesis es más corta que las anteriores y simula el aislamiento de una placa con múltiples ABHs, en el rango de media y alta frecuencia. A tal efecto se emplea el método del análisis estadístico de distribución modal de energía (SmEdA: statistical modal energy distribution analysis). En esta sección, la estructura con ABHs ya no se analiza como un elemento individual, sino que se acopla a dos cavidades de aire formando parte de un sistema mecánico más complejo. A lo largo de la tesis se utiliza repetidamente el método de expansión gaussiana (GEM: Gaussian expansión method). Por GEM entendemos tomar funciones gaussianas como base para resolver ecuaciones diferenciales en derivadas parciales en el marco del método de Rayleigh-Ritz. El GEM se parece mucho a los enfoques de ondículas, pero ofrece algunas ventajas en el caso de condiciones de contorno periódicas. Al principio de la tesis se expone un breve repaso del GEM y, cuando es necesario, se aborda su reformulación para un problema particular en el capítulo correspondiente.
Acoustic black holes (ABHs) in mechanics usually consist of geometrical indentations on beams and plates having a power-law decreasing thickness profile. An ABH slows down the phase and group velocity of incident flexural waves in such a way that, ideally, it would take an infinite amount of time for them to reach the ABH center, if the latter had an exact zero thickness. Though this is not possible in practice, strong wave dissipation can be achieved by placing a damping layer at the central region of the ABH, where most vibration energy concentrates. In recent years, ABHs have been not only exploited as a passive means for structural vibration and noise reduction, but its potential for other applications like wave manipulation or energy harvesting have been also explored. The objective of this thesis is threefold. Therefore, after an initial overview the work is divided into three main parts. The first one deals with ABH applications on straight beams and flat plates. To start with, an ABH piezoelectric bimorph cantilever for energy harvesting is proposed and analyzed. Then, ring-shaped ABH indentations are suggested as a means of isolating external excitation points in flat plates and prevent vibration transmission. Finally, periodic ABH array configurations are contemplated to collimate flexural wave beams and focus energy at desired plate locations. The second part of the thesis proposes new ABH designs for curved structures. The latter are very common in the naval, aeronautical and industrial sectors so it is worth investigating if ABHs could function for them. The section starts analyzing the embedding of ABHs on circular beams and how this results in the appearance of typical phenomena of periodic systems. After that, an annular ABH is proposed to reduce vibrations in cylindrical shells. The cases of a simply supported shell with an annular ABH indentation and of a periodic simply supported ABH shell with stiffeners are considered. To finish the section, the effects of annular ABHs on sound radiation are investigated in terms of sound power level, radiation efficiency and supersonic intensity. The third part of the thesis is shorter than the previous ones and is devoted to analyzing the transmission loss of a plate with multiple ABH indentations, in the mid-high frequency range. Statistical modal energy distribution analysis is used for that purpose. Here, the ABH plate is not taken as an individual structure but coupled to two air cavities, thus being part of a more complex mechanical system. Throughout the thesis repeated use is made of the Gaussian expansion method (GEM). The GEM refers to taking Gaussian functions as the basis for solving partial differential equations in the framework of the Rayleigh-Ritz method. The GEM closely resembles wavelet approaches but offers some advantages in the case of periodic boundary conditions. A brief overview of the GEM is exposed at the beginning of the thesis and, when necessary, its reformulation for a particular problem is tackled in its corresponding chapter.

This thesis work focuses on the dynamical properties of two-component galaxy models characterized by a stellar density distribution described by a Jaffe profile, and a galaxy (stars plus dark matter) density distribution following a r^(-3) shape at large radii. The dark matter (hereafter, DM) density profile is defined by the difference between the galaxy and the stellar profiles. The orbital structure of the stellar component is described by the Osipkov-Merritt (OM) radial anisotropy, and that of the DM halo is assumed isotropic; a black hole (BH) is also added at the center of the galaxy. The thesis is organized as follows. In Chapter 2 the main structural properties of the models are presented, and the conditions required to have a nowhere negative and monothonically decreasing DM halo density profile are derived; a discussion is also given of how the DM component can be built in order to have the same asymptotical behaviour, in the outer regions and near the center, as the Navarro-Frenk-White (NFW) profile. In Chapter 3 an investigation of the phase-space properties of the models is carried out, both from the point of view of the necessary and sufficient conditions for consistency, and from the direct inspection of the distribution function; the minimum value of the anisotropy radius for consistency is derived in terms of the galaxy parameters. In Chapter 4 the analytical solution of the Jeans equations with OM anisotropy is presented, together with the projection of the velocity dispersion profile at small and large radii. Finally, in Chapter 5 the global quantities entering the Virial theorem are explicitly calculated; these can be used for energetic considerations that are briefly mentioned, and allow us to determine the fiducial anisotropy limit required to prevent the onset of Radial Orbit Instability as a function of the galaxy parameters. The main results are summarized in Chapter 6, and some technical details are given in the Appendices.

Au long de ce manuscrit de thèse je présenterai des effets non linéaires émergents dans les condensats d'exciton-polaritons spineurs. Après un chapitre d'introduction amenant les notions de bases nécessaires, je me concentrerai dans une première partie sur les défauts topologiques quantifiés par des nombres demi-entiers et discuterai leur stabilité, accélération et nucléation en présence de champs magnétiques effectifs. Nous verrons que ces objets se comportent comme des charges magnétiques manipulables démontrant une analogie fascinante avec les monopoles de Dirac. De manière remarquable nous verrons également que ces objets peuvent être utilisés comme des signaux stables pour sonder la physique d'analogues acoustiques de trous noirs. Dans une seconde partie j'étudierai des structures de basse dimensions. Plus particulièrement, je décrirai la formation de solitons de bande interdite et les oscillations de Bloch des exciton-polaritons dans des microfils comportant des structures périodiques et d'autre part les oscillations Josephson à température ambiante dans des paires de micropilliers couplés.

Nous analysons des bulles d'espace-temps d'épaisseur finie en relativité générale. Les conditions d'énergie sont utilisées afin d'obtenir un ensemble de critères permettant de restreindre la structure du bord de la bulle. Dans le cas des bulles statiques et à symétrie sphérique, nous obtenons quatre inégalités différentielles équivalentes aux trois conditions d'énergie les plus communes. Nous montrons qu'elles sont équivalentes à un ensemble de deux inégalités différentielles simples lorsque le potentiel gravitationnel effectif a une forme particulière. Nous paramétrons alors l'espace-temps de manière à rendre la vérification de ces inégalités plus simple lorsqu'il sera question de bulles d'espace-temps. Nous traitons en particulier quatre formes de bulles, toutes caractérisées par un extérieur de type Schwarzschild de Sitter. Nous montrons que notre méthode donne les bons résultats lorsque la limite où l'épaisseur de la bulle tend vers zéro est prise. Nous terminons par un traitement succinct du problème d'une onde gravitationnelle se propageant dans un nuage de bulles d'espace-temps.
We analyze space-time bubbles of finite thickness in general relativity. We use the energy conditions to restrict their structures. In the case of static, spherically symmetric bubbles, we get a set of four differential inequalities. If the effective gravitational potential is taken of a particular form, we show that they can be further reduced to a set of two differential inequalities. We then parameterize the bubble's wall in a particular way, simplifying the inequalities, and easing the application of boundary conditions on our solutions. We then treat four different cases of bubbles that all have a Schwarzschild de Sitter exterior. We show that in the limit where the thickness of the bubble's wall goes to zero, we recover the standard results. Lastly, we treat gravitational waves propagating in a dilute gas of non-interacting space-time bubbles.

The subject of study of this thesis is the Kerr-Newman-(anti-)de Sitter space- time, a rotating and charged exact black-hole solution of the Einstein-Maxwell equations with a non-zero cosmological constant. In the first part of the thesis we examine admissible extremal configurations, present the corresponding Penrose diagrams, and investigate the effects of frame-dragging. In the second part, we follow the motion of charged particles via the Lagrangian formalism, focusing on the equatorial plane and the axis where we arrived at some analytic results con- cerning the trajectories. Static particles, effective potentials and - in the case of the equatorial plane - stationary circular orbits are examined. We also perform numerical simulations of particle motion to be able to check our analytic results and also to foster our intuition regarding the behaviour of the test particles. The last part concerns quantum tunnelling of particles through the space-time's hori- zons, specifically the null geodesic method. The main goal of these computations is to obtain horizon temperatures, in which we succeed up to a constant multi- plicative factor. We discuss various pitfalls of the method and stake out a possible approach when applying it to the extreme horizons present in KN(a)dS. 1

碩士
國立清華大學
物理系
101
The phase structure of Kerr-AdS black holes is studied at three different temperatures, $T_{c1}$, $T_{c2}$ and $T_L$. At $T_{c1}$, a second order phase transition is identified to be in the same universality class as the van der Waals liquid-gas system. We derive the critical exponents ($\alpha$, $\beta$, $\gamma$, $\delta$)=(0, $\frac{1}{2}$, 1, 3) associated to this phase transition, and discuss the free energy and the scaling symmetry near the critical point. $T_L$ is the lowest temperature under which a Kerr-AdS black hole could reduce to a Schwarzschild-AdS black hole, and this temperature correspond to the critical temperature determined in the Hawking-Page phase transition. $T_{c2}$ is the temperature which separates the stable and partially unstable isotherms. Along with $T_{c2}$, we found an asymptotic value of angular momentum $\Omega_0$ = $1/l$ as $J$ goes to infinity. This asymptotic value reminisces us the minimal value of the molecule volume $V_0$ in the van der Waals liquid-gas system.

In general relativity, black hole is the simplest macroscopic object in the universe: any black hole can be completely described by its mass, charge and angular mo- mentum. However, such a simple picture might be changed if the gravitational field equations are modified or quantum effects are taken into consideration. These additional hairs of black hole, if exist, may provide valuable information to reveal the deepest mystery of the universe: quantum theory of gravity.

In this thesis, we try to relate the hypothetical extra hairs of black hole with the ob- servational evidence as gravitational waves – another prediction of general relativity and are recently detected. In Chapter I, we provide a pedagogical introduction to the black hole hairs introduced by modified gravity and quantum mechanics, and lay out a mathematical framework to describe the gravitational wave emission with the existence of near-horizon quantum hair. In Chapter II we show that in scalar-tensor theory of gravity, the formation process of a black hole from gravitational collapse is accompanied with the emission of scalar hair. This mechanism gives rise to a scalar type memory effect of gravitational wave, which does not exist in general relativity. This phenomenon can further be used to study the parameter space of the scalar-tensor theory. In Chapter III, we find the scalar gravitational memory effect from stellar collapses provide the strongest sources for the stochastic gravita- tional wave background with scalar polarization in Brans-Dicke theory. The energy density spectrum for this background is provided and its model dependencies are studied. In Chapter IV, we provide a Green’s function method to study the echoes, which are the gravitational waves reflected by the quantum hair near the event hori- zon of a black hole. In Chapter V, we build phenomenological models to describe the near-horizon quantum hair and predict its implication to the binary black hole stochastic gravitational wave background. Our study indicates that the existence of the quantum hair will significantly increases such a background and pins down the most relevant model parameter to be the area under the effective potential. Further, we also demonstrate that the result is rather robust against the uncertainties about the nature of the near-horizon quantum hair. In the end, a field theory based treatment to the gravitational waves in general relativity is provided as the appendix.

Classical theory cannot provide a satisfying scenario for a unitary thermodynamic evolution of black holes. To preserve information one requires quantum mechanical effects on scales reaching beyond the traditional horizon radius. Therefore, common to many of the theories attempting to resolve the paradox is the existence of exotic horizon structures. The recent advent of gravitational wave astronomy provides a possible means for detecting the existence of such structures through gravitational wave emission in the ringdown phase of binary black hole mergers. Such emission is described by quasinormal modes (QNMs) in which the gravitational waves originates outside the black hole, in the vicinity of the photon spheres. Requiring reflective properties of the horizon structure results in the existence of gravitational echoes that may be detected by facilities such as LIGO etc.. This thesis studies geodesic motion of such echoes in the equatorial plane of a rotating black hole. Depending on the extent of the horizon structure, and the particular mode of emission, one can expect different timescales for the echoes. For a horizon structure extending    outside the traditional horizon of a  ,  black hole one would ideally find echoes appearing as integer multiples of  after the primary signal. The time delay is expected to increase by at least an order of magnitude if one lets . The expected echo timescales for gravitational waves emitted from any point around the black hole, in arbitrary modes, is an interesting further study.

Remarkably, the central regions of galaxies are very important in shaping and influencing galaxies as a whole. As such, galaxy cores can be used for classification, to determine which processes may be important in galaxy formation and evolution. Past studies, for example, have found a dichotomy in the inner slopes of early-type galaxy surface brightness profiles. Using deprojections of the galaxies from the ACS Virgo and Fornax Cluster Surveys (ACSVCS/FCS), we show that, in fact, this dichotomy does not exist. Instead, we demonstrate that the brightest early-type galaxies tend to have central light deficits, a trend which gradually transitions to central light excesses – also known as compact stellar nuclei – as we go to fainter galaxies. This effect is quantified, and can be used to determine what evolutionary factors are important as we move along the galaxy luminosity function. The number of stellar nuclei that we observe is, in fact, an unexpected result emerging from the ACSVCS/FCS. Being three times more common than previously thought, they are present in the vast majority of intermediate and low-luminosity galaxies. Conversely, it has been known for over a decade that there is likely a supermassive black hole weighing millions to billions of solar masses at the center of virtually every galaxy of sufficient size. These black holes are known to follow scaling relations with their host galaxies. Using the ACSVCS, along with new kinematical data from long-slit spectroscopy, we measure the dynamical masses of 83 galaxies, and show that supermassive black holes and nuclei appear to fall along the same scaling relation with host mass. Both represent approximately 0.2% of their host’s mass, implying an important link between the two types of central massive objects. Finally, we extract elliptical isophotes and fit parameterized models to the surface brightness profiles of new Hubble Space Telescope imaging of the ACSVCS galaxies, observed in infrared and ultraviolet bandpasses. Taken together, the two surveys represent an unprecedented collection of isophotal and structural parameters of early-type galaxies, and will allow us to learn a great deal about the stellar populations and formation histories of galaxy cores.
Graduate

Tesis (Doctor en Física)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación, 2018.
En el marco del problema de estabilidad de agujeros negros, esta tesis trata diversos aspectos de las ecuaciones de campos libres sin masa sobre espacio-tiempos curvos, con énfasis en espacios algebraicamente especiales que contienen agujeros negros como soluciones particulares. El enfoque central es el estudio de la posible correspondencia entre campos escalares y campos de spin superior, y de la existencia y origen de simetrías ocultas y ciertos mecanismos asociados a la teoría de twistors. Encontramos fórmulas explícitas de esta correspondencia, y mostramos que el patrón de simetrías subyacente se entiende desde el punto de vista de la covariancia conforme y la existencia de estructuras complejas en el espacio-tiempo. Analizamos también aspectos de estabilidad de los campos en el caso de agujeros negros estáticos asintóticamente anti-de Sitter. Estudiamos espacio-tiempos tanto de cuatro como de altas dimensiones.
In the context of the black hole stability problem, this thesis deals with several aspects of the massless free field equations on curved spacetimes, with emphasis on algebraically special spaces that contain black hole solutions as particular cases. The main approach is the study of the possible correspondence between scalar fields and higher spin fields, and of the existence and origin of hidden symmetries and certain mechanisms associated to twistor theory. We find explicit formulas for this correspondence, and we show that the underlying symmetry pattern is understood from the point of view of conformal covariance and the existence of complex structures on the spacetime. We also analyze aspects of the stability of the fields in the case of asymptotically anti-de Sitter static black holes. We study spacetimes of both four and higher dimensions.

Text in English
The aim of this research is to assess the impact social capital has had on Somali businesses. It argues against the perception that Somali business expertise is derived solely from the principles of economics. It argues that social capital plays a pivotal role in shaping the Somali spirit of entrepreneurship. The role of social capital in the creation of Somali human and financial capital is examined. This thesis, being a qualitative study, used semi-structured, unstructured interviews and direct observation as data collection methods.
Sociology
M.A. (Sociology)