Dissertations / Theses on the topic 'Classical gravity'

Einstein’s General Relativity has been our best theory of gravity for nearly a century, yet we know it cannot be the final word. In this thesis, we consider modifications to General Relativity, motivated by both high and low energy physics. In the quantum realm, we focus on Horava gravity, a theory which breaks Lorentz invariance in order to obtain good ultraviolet physics by adding higher spatial derivatives to the action (improving propagator behaviour in loops) but not temporal (avoiding Ostrogradski ghosts). By using the Stückelberg trick, we demonstrate the necessity of introducing a Lorentz violating scale into the theory, far below the Planck scale, to evade strong coupling concerns. Using this formalism we then show explicitly that Horava gravity breaks the Weak Equivalence Principle, for which there are very strict experimental bounds. Moving on to considering matter in such theories, we construct DiffF(M) invariant actions for both scalar and gauge fields at a classical level, before demonstrating that they are only consistent with the Equivalence Principle in the case that they reduce to their covariant form. This motivates us to consider the size of Lorentz violating effects induced by loop corrections of Horava gravity coupled to a Lorentz invariant matter sector. Our analysis reveals potential light cone fine tuning problems, in addition to evidence that troublesome higher order time derivatives may be generated. At low energies, we demonstrate a class of theories which modify gravity to solve the cosmological constant problem. The mechanism involves a composite metric with the square root of its determinant a total derivative or topological invariant, thus ensuring pieces of the action proportional to the volume element do not contribute to the dynamics. After demonstrating general properties of the proposal, we work through a specific example, demonstrating freedom from Ostrogradski ghosts at quadratic order (in the action) on maximally symmetric backgrounds. We go on to demonstrate sufficient conditions for a theory in this class to share a solution space equal to that of Einstein’s equations plus a cosmological constant, before determining the cosmology these extra solutions may have when present.

Despite remarkable progress made in the past century, which has revolutionized our understanding of the universe, there are numerous open questions left in theoretical physics. Particularly important is the fact that the theories describing the fundamental interactions of nature are incompatible. Einstein's theory of general relative describes gravity as a dynamical spacetime, which is curved by matter and whose curvature determines the motion of matter. On the other hand we have quantum field theory, in form of the standard model of particle physics, where particles interact via the remaining interactions - electromagnetic, weak and strong interaction - on a flat, static spacetime without gravity. A theory of quantum gravity is hoped to cure this incompatibility by heuristically replacing classical spacetime by quantum spacetime'. Several approaches exist attempting to define such a theory with differing underlying premises and ideas, where it is not clear which is to be preferred. Yet a minimal requirement is the compatibility with the classical theory, they attempt to generalize. Interestingly many of these models rely on discrete structures in their definition or postulate discreteness of spacetime to be fundamental. Besides the direct advantages discretisations provide, e.g. permitting numerical simulations, they come with serious caveats requiring thorough investigation: In general discretisations break fundamental diffeomorphism symmetry of gravity and are generically not unique. Both complicates establishing the connection to the classical continuum theory. The main focus of this thesis lies in the investigation of this relation for spin foam models. This is done on different levels of the discretisation / triangulation, ranging from few simplices up to the continuum limit. In the regime of very few simplices we confirm and deepen the connection of spin foam models to discrete gravity. Moreover, we discuss dynamical, e.g. diffeomorphism invariance in the discrete, to fix the ambiguities of the models. In order to satisfy these conditions, the discrete models have to be improved in a renormalisation procedure, which also allows us to study their continuum dynamics. Applied to simplified spin foam models, we uncover a rich, non--trivial fixed point structure, which we summarize in a phase diagram. Inspired by these methods, we propose a method to consistently construct the continuum theory, which comes with a unique vacuum state.
Trotz bemerkenswerter Fortschritte im vergangenen Jahrhundert, die unser Verständnis des Universums revolutioniert haben, gibt es noch zahlreiche ungeklärte Fragen in der theoretischen Physik. Besondere Bedeutung kommt der Tatsache zu, dass die Theorien, welche die fundamentalen Wechselwirkungen der Natur beschreiben, inkompatibel sind. Nach Einsteins allgemeiner Relativitätstheorie wird die Gravitation durch eine dynamische Raumzeit dargestellt, die von Materie gekrümmt wird und ihrerseits durch die Krümmung die Bewegung der Materie bestimmt. Dem gegenüber steht die Quantenfeldtheorie, die die verbliebenen Wechselwirkungen - elektromagnetische, schwache und starke Wechselwirkung - im Standardmodell der Teilchenphysik beschreibt, in dem Teilchen auf einer statischen Raumzeit -- ohne Gravitation -- miteinander interagieren. Die Hoffnung ist, dass eine Theorie der Quantengravitation diese Inkompatibilität beheben kann, indem, heuristisch, die klassische Raumzeit durch eine 'Quantenraumzeit' ersetzt wird. Es gibt zahlreiche Ansätze eine solche Theorie zu definieren, die auf unterschiedlichen Prämissen und Ideen beruhen, wobei a priori nicht klar ist, welche zu bevorzugen sind. Eine Minimalanforderung an diese Theorien ist Kompatibilität mit der klassischen Theorie, die sie verallgemeinern sollen. Interessanterweise basieren zahlreiche Modelle in ihrer Definition auf Diskretisierungen oder postulieren eine fundamentale Diskretheit der Raumzeit. Neben den unmittelbaren Vorteilen, die Diskretisierungen bieten, z.B. das Ermöglichen numerischer Simulationen, gibt es auch gravierende Nachteile, die einer ausführlichen Untersuchung bedürfen: Im Allgemeinen brechen Diskretisierungen die fundamentale Diffeomorphismensymmetrie der Gravitation und sind in der Regel nicht eindeutig definiert. Beides erschwert die Wiederherstellung der Verbindung zur klassischen, kontinuierlichen Theorie. Das Hauptaugenmerk dieser Doktorarbeit liegt darin diese Verbindung insbesondere für Spin-Schaum-Modelle (spin foam models) zu untersuchen. Dies geschieht auf sehr verschiedenen Ebenen der Diskretisierung / Triangulierung, angefangen bei wenigen Simplizes bis hin zum Kontinuumslimes. Im Regime weniger Simplizes wird die bekannte Verbindung von Spin--Schaum--Modellen zu diskreter Gravitation bestätigt und vertieft. Außerdem diskutieren wir dynamische Prinzipien, z.B. Diffeomorphismeninvarianz im Diskreten, um die Ambiguitäten der Modelle zu fixieren. Um diese Bedingungen zu erfüllen, müssen die diskreten Modelle durch Renormierungsverfahren verbessert werden, wodurch wir auch ihre Kontinuumsdynamik untersuchen können. Angewandt auf vereinfachte Spin-Schaum-Modelle finden wir eine reichhaltige, nicht-triviale Fixpunkt-Struktur, die wir in einem Phasendiagramm zusammenfassen. Inspiriert von diesen Methoden schlagen wir zu guter Letzt eine konsistente Konstruktionsmethode für die Kontinuumstheorie vor, die einen eindeutigen Vakuumszustand definiert.

It is proved that Taub-Bolt infillings are double-valued whereas Taub-Nut and Eguchi-Hanson infillings are unique in arbitrary dimensions. In the case of trivial bundles, there are two or no Schwarzschild infillings. The condition of whether a particular type of infilling exists can be expressed as a limitation on squashing through a functional dependence on dimension in each case. The case of the Eguchi-Hanson metric is solved in arbitrary dimension. The Taub-Nut and the Taub-Bolt are solved in four dimensions and methods for higher dimensions are discussed. For the case of Schwarzschild in arbitrary dimension, thermodynamic properties of the two infilling black-hole solutions are discussed and analytic formulae for their masses are obtained using higher order hypergeometric functions. Convexity of the infilling solutions and isoperimetric inequalities involving the volume of the boundary and the volume of the infilling solutions are investigated. In particular, analogues of Minkowski’s celebrated inequality in flat space are found and discussed. In Chapters 3, the Dirichlet problem is studied for an SU (2) x U(1)-invariant S³ boundary within the class of self-dual Taub-Nut-(anti) de Sitter metrics. Including complex ones there can be a total of three solutions for the infilling although there will be a unique real solution or no real solution depending on the boundary data - the two radii of the S³. Exact solutions of the infilling geometries are obtained making its possible to find their Euclidean actions as analytic functions of the two radii of the S³-boundary. The case of L < 0 is investigated further. For reasonable squashing of the S³, all three infilling solutions have real-valued actions which possess a “cusp catastrophe” structure with a “catastrophe manifold” that shows that the unique real positive-definite solution dominates. The necessary and sufficient condition for the existence of the positive-definite solution is found as a condition on the two radii of the S³. In Chapter 4, the same boundary-value problem is studied for the Taub-Bolt-anti-de Sitter metrics. Such metrics are obtained from the two-parameter Taub-NUT-anti de Sitter family. The condition of regularity results in two bifurcated one-parameter family. It is found that any axially symmetric S³-boundary can be filled in with at least one solution coming from each of these two branches. The infillings appear or disappear catastrophically in pairs as the values of the two radii of S³ are varied; this happens simultaneously for both branches. It is found that the total number in independent infillings is two, six or ten. When the two radii are of the same order and large this number is two. In the isotropic limit, i.e., for round S³ this holds for small radii as well. In Chapter 5, the Dirichlet problem is studied within Euclideanised Schwarzschild-anti de Sitter and anti de Sitter metrics, i.e., for an S¹ x Sⁿ boundary. For such boundary data there exist two or no black-holes and always a unique anti de Sitter solution. The black holes have strictly positive and negative specific heats (and hence locally thermodynamically stable and unstable respectively). It is shown that for any radius of the cavity, the larger hole can be globally thermodynamically stable above a critical temperature by demonstrating that a phase transition occurs from hot AdS to Schwarzschild-AdS within the cavity. This gives the Hawking-Page phase transition in the infinite cavity limit. It is found that the case of five dimensions is special in that the masses of the two black holes, and hence other quantities of classical and semi-classical interest, can be obtained exactly as functions of cavity radius and temperature. It is also possible in this case to obtain the minimum temperature (below which no black holes exist) and the critical temperature for phase transition as analytic functions of cavity-radius. In Chapter 6, cosmological and instanton solutions are found for CP¹ and CP² sigma models coupled to gravity with a possible cosmological constant.

The formulation of a consistent scheme for treating semiclassical systems is considered, giving particular emphasis to the case of gravity. A critical review of the semiclassical problem is first given, stressing the conceptual aspects of the topic; the theory usually adopted is found to be unsatisfactory, and the need to have an unambiguous interpretation of quantum mechanics before trying to give an alternative description is realized. Our way to arrive at such an interpretation is rather unusual, but it presents the advantage of being almost compelling in the choice to make: First, we reformulate the Schrodinger equation as a set of hydrodynamical equations involving quantities which formally play the role of mass density, velocity and pressure for a fluid; the problem of interpreting the wave function is thus reduced to that of interpreting these quantities. We then show how they can be derived from the Wigner distribution function exactly as in the usual formalism of kinetic theory, and discuss how this fact provides strong support in favour of the statistical interpretation of quantum theory, according to which the state vector describes only ensembles, and not individual systems. We also consider some implications of these results on the possible existence of a more fundamental theory underlying quantum mechanics. It is shown that reconsidering the semiclassical problem in the light of the statistical interpretation, one is led to distinguish between a strongly and a weakly semiclassical regime, which are essentially characterized by the size of the statistical dispersion induced in the observables of the classical subsystem by the coupling to the quantum one. It turns out that in the weakly semiclassical regime, in which this dispersion is not negligible, the concept of coupling equations cannot be successfully applied, and one has rather to define a probability distribution even for the values of the classical observables; an hypothesis which allows to specify such a distribution is enunciated. Several examples of the application of these general principles are considered, and it is shown how the treatment of semiclassical relativistic fields requires a much more sophisticated treatment of the quantum source. This is provided reformulating quantum theory in terms of a quasiprobability functional P[1] in the space of the histories of the system. It is shown how such a functional allows to reconstruct the usual phase space distributions when integrated over suitable sets of paths, in a way which clarify the relations between operator ordering, path integration and phase space treatment of quantum theory. The relativistic extension of p[f] is also constructed, and an explicitly covariant version of relativistic quantum theory is discussed in some details. It is shown how the latter allows, formally, to consider superpositions of different mass eigenstates, although such superpositions are not directly observable. Finally, the application of these new techniques to the treatment of semiclassical electromagnetism and gravity, as well as of a scalar field, are considered. It is shown how the usual semiclassical field equations, suitably reinterpreted in terms of averages of the field, are recovered either in linear cases or in the strongly semiclassical regime, but that they do not hold in general. Finally, some possible extensions and implications of the formalism are discussed.

We consider the stability of black holes within both classical general relativity and the semiclassical thermodynamic description. In particular, we study linearised perturbations and their contribution to the gravitational partition function, addressing technical issues for charged (Reissner-Nordstrom) and rotating (Kerr-AdS) black holes. Exploring the connection between classical and thermodynamic stability, we find classical instabilities of Myers-Perry black holes and bifurcations to new black hole families.

This thesis explores three different aspects of quantum gravity. First we study D3-brane black holes in Calabi-Yau compactifications of type IIB string theory. Using the OSV conjecture and a relation between topological strings and matrix models we show that some black holes have a matrix model description. This is the case if the attractor mechanism fixes the internal geometry to a conifold at the black hole horizon. We also consider black holes in a flux compactification and compare the effects of the black holes and fluxes on the internal geometry. We find that the fluxes dominate. Second, we study the scalar potential of type IIB flux compactifications. We demonstrate that monodromies of the internal geometry imply as a general feature the existence of long series of continuously connected minima. This allows for the embedding of scenarios such as chain inflation and resonance tunneling into string theory. The concept of monodromies is also extended to include geometric transitions: passing to a different Calabi-Yau topology, performing its monodromies and then returning to the original space allows for novel transformations. All constructions are performed explicitly, using both analytical and numerical techniques, in the mirror quintic Calabi-Yau. Third, we study cosmological topologically massive gravity at the chiral point, a prime candidate for quantization of gravity in three dimensions. The prospects of this scenario depend crucially of the stability of the theory. We demonstrate the presence of a negative energy bulk mode that grows logarithmically toward the AdS boundary. The AdS isometry generators have non-unitary matrix representations like in logarithmic CFT, and we propose that the CFT dual for this theory is logarithmic. In a complementing canonical analysis we also demonstrate the existence of this bulk degree of freedom, and we present consistent boundary conditions encompassing the new mode.

I modify the quasilocal energy formalism of Brown and York into a purely Hamiltonian form. As part of the reformulation, I remove their restriction that the time evolution of the boundary of the spacetime be orthogonal to the leaves of the time foliation. Thus the new formulation allows an arbitrary evolution of the boundary which physically corresponds to allowing general motions of the set of observers making up that boundary. I calculate the rate of change of the quasilocal energy in such situations, show how it transforms with respect to boosts of the boundaries, and use the Lanczos-Israel thin shell formalism to reformulate it from an operational point of view. These steps are performed both for pure gravity and gravity with attendant matter fields. I then apply the formalism to characterize naked black holes and study their properties, investigate gravitational tidal heating, and combine it with the path integral formulation of quantum gravity to analyze the creation of pairs of charged and rotating black holes. I show that one must use complex instantons to study this process though the probabilities of creation remain real and consistent with the view that the entropy of a black hole is the logarithm of the number of its quantum states.

La gravitation quantique à boucle covariante (CLQG) est une théorie spéculative de la gravitation quantique qui a émergé de plusieurs directions de recherche différentes. Récemment, elle a été appliquée à la transition dite trou noir/trou blanc – un modèle particulier d’effondrement stellaire qui résout le problème de l’information et conduit potentiellement à des effets observables. Cependant, plusieurs obstacles conceptuels et informatiques ont entravé les recherches sur ce scénario physique.Cette thèse aborde certaines de ces questions : une mesure d’intégration pour les états du noyau de la chaleur dans la paramétrisation de géométrie twistée est dérivée, ce qui est nécessaire pour définir des observables physiques, un algorithme de triangulation simplicial pour des variétés de topologie I x Σ est décrit et une nouvelle méthode est développée pour calculer les amplitudes de transition holomorphes en l’absence de points critiques. Cette nouvelle méthode peut être vue comme un développement semi-classique des amplitudes de CLQG autour d’un espace-temps classique
Covariant Loop Quantum Gravity (CLQG) is a tentative theory of quantum gravity which has emerged from a number of different research directions. Recently, it has been applied to the so-called black hole to white hole transition – a particular model of stellar collapse which resolves the information puzzle and potentially leads to observable effects. However, several conceptual and computational obstacles have impeded progress in the investigation of this physical scenario.This thesis addresses some of these issues: An integration measure for heat kernel states in the twisted geometry parametrization is derived which is necessary to define physical observables, a simplicial triangulation algorithm for manifolds of topology I x Σ is described and a new method is developed for computing holomorphic transition amplitudes in the absence of critical points. This new method can be seen as a semi-classical expansion of CLQG amplitudes around a classical background spacetime

Depuis 1916, l'étude des Trous Noirs a soulevé des questions intrigantes. Seulement certaines ont été résolues. En effet, nous faisons face à des régimes où s’entremêlent la théorie quantique et l'espace-temps. Les TN comme porte d'entrée pour comprendre la nature quantique de la gravité. Ma thèse a été entièrement dédiée à ce domaine central de la physique théorique, avec pour but la compréhension la plus large possible des débats autour de ces questions. C'est ainsi qu'ont été produits des résultats originaux qui constituent le cœur de ce manuscrit. 1-Les surfaces de volume maximal des TN sont étudiées. Un TN astrophysique terminera sa vie avec une aire planckienne de $10^{-70} m^2$ dissimulant $10^5$ fois le volume de l'univers observable. Ceci peut avoir des conséquences sur la viabilité du "remnant scenario" comme solution au paradoxe de l'information. 2-Le scénario "trou-noir-trou-blanc" est fortement instable. Une modification minimale est proposée pour résoudre ce problème. 3-Une généralisation des quatre lois de la thermodynamique des TN est démontrée pour des cônes de lumière s'intersectant dans un espace de Minkowski. 4-On étudie des espaces conformellement plats où de telles lois acquièrent une interprétation thermodynamique standard. Le plus simple est l'espace-temps de Bertotti-Robinson, connu pour encoder la géométrie proche de l'horizon d'un TN chargé. 5-Pour peu que le bon tenseur énergie-impulsion soit identifié, les équations du champ Einstein-Cartan peuvent être retrouvées comme l'équation d'état d'un équilibre thermodynamique, comme dans le cas original de la RG. Ces résultats contribuent au débat intense sur les questions cruciales posées ci-dessus
Since 1916 intriguing questions have arisen from the study of Black Holes (BH). Only some of them have been resolved. Indeed, we are faced with regimes where the yet unknown interplay between quantum theory and spacetime unveils. BH physics is a gateway to the quantum nature of gravity. My thesis has been completely devoted to this central domain of theoretical physics, with the guiding aim of understanding in the widest possible manner the debate around those questions. The process has produced original results that constitute the main core of the manuscript. 1- The maximal volume surfaces of evaporating BHs are studied. An astrophysical BH will end its life with an external planckian area $10^{-70} m^2$ hiding $10^5$ times the volume of our observable Universe. This can have consequences on the viability of the “remnant scenario” as solution to the BH information paradox. 2- The “black-hole-to-white-hole scenario” is analyzed. The model is shown to be strongly unstable, and a minimal resolutive modification is proposed. 3- A generalisation of the four laws of BH thermodynamics is proven for intersecting light cones in Minkowski spacetime. 4- Conformally flat spaces where such laws acquire the standard thermodynamical interpretation are studied. The simplest one is the Bertotti-Robinson spacetime, known to encode the near-horizon geometry of a charged BH. 5- It is shown that, if the correct energy-momentum tensor is identified, the Eintein-Cartan’s field equations can be recovered as a thermodynamical equilibrium equation of state just like in the GR original case. Such results contribute to the intense debate on the opening crucial questions

The present thesis is divided into two parts. Part I is devoted to the study of Gribov ambiguity in gauge systems and its relation with the appearance of degeneracies in the symplectic structure of the corresponding reduced phase space after gauge fixation. Part II is concerned with classical dual field theories for three-dimensional Einstein gravity and the symplectic structure on coadjoint orbits of the corresponding asymptotic symmetry group.In Part I, the Gribov problem is studied in the context of finite temperature QCD and the structure of the gluon propagator is analyzed. The standard confined scenario is found for low temperatures, while for high enough temperatures deconfinement takes place and a free gluon propagator is obtained. Subsequently, the relation between Gribov ambiguity and degeneracies in the symplectic structure of gauge systems is analyzed. It is shown that, in finite-dimensional systems, the presence of Gribov ambiguities in regular constrained systems always leads to a degenerate symplectic form upon Dirac reduction. The implications for the Gribov-Zwanziger approach to QCD and the symplectic structure of the theory are discussed. In Part II, geometrical actions for three-dimensional Einstein gravity are constructed by studying the symplectic structure on coadjoint orbits of the asymptotic symmetry group. The geometrical action coming from the Kirillov-Kostant symplectic form on coadjoint orbits is analyzed thought Dirac's algorithm for constrained systems. By studying the case of centrally extended groups and semi-direct products, the symplectic structure on coadjoint orbits of the Virasoro and the BMS3 group are analyzed. This allows one to associate separate geometric actions to each coadjoint orbit of the solution space, leading to two-dimensional dual fiel theories for asymptotically AdS and asymptotically flat three-dimensional gravity respectively.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

The objective of this thesis is to study classical and quantum aspects of infinite derivative field theories and infinite derivative gravity. In- finite derivative theories of gravity can be made free from ghosts and classical singularities. In order to avoid ghosts, one modifies the graviton propagator by employing entire functions so that no new poles are introduced apart from the pole corresponding to the massless graviton of General Relativity. Inspired by infinite derivative gravity, we consider an infinite derivative scalar toy model and demonstrate renormalisability when the loop-order is arbitrarily large. Moreover, scattering diagrams within the framework of infinite derivative field theories are explicitly evaluated and it is shown that the cross section can be made finite. Finally, we perform a Hamiltonian analysis of an infinite derivative gravitational theory with a simpler action containing only the Ricci scalar and compute the number of relevant degrees of freedom.

The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the `super-accelerated' scenario not excluded by observations, thus exploring alternatives to the standard LambdaCDM scenario. The second part concerns the spinfoam approach to (Loop) Quantum Gravity, which is an attempt to provide a `sum-over-histories' formulation of gravitational quantum transition amplitudes. The research here presented focuses on the face amplitude of a generic spinfoam model for Quantum Gravity.

The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the `super-accelerated' scenario not excluded by observations, thus exploring alternatives to the standard LambdaCDM scenario. The second part concerns the spinfoam approach to (Loop) Quantum Gravity, which is an attempt to provide a `sum-over-histories' formulation of gravitational quantum transition amplitudes. The research here presented focuses on the face amplitude of a generic spinfoam model for Quantum Gravity.

In this thesis we accomplish two goals: We construct a two dimensional conformal field theory (CFT), in the form of a Liouville theory, in the near horizon limit for three and four dimensions black holes. The near horizon CFT assumes the two dimensional black hole solutions that were first introduced by Christensen and Fulling (1977 Phys. Rev. D 15 2088-104) and later expanded to a greater class of black holes via Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303). The two dimensions black holes admit a $Diff(S^1)$ or Witt subalgebra, which upon quantization in the horizon limit becomes Virasoro with calculable central charge. These charges and lowest Virasoro eigen-modes reproduce the correct Bekenstein-Hawking entropy of the four and three dimensions black holes via the Cardy formula (Bl"ote et al 1986 Phys. Rev. Lett. 56 742; Cardy 1986 Nucl. Phys. B 270 186). Furthermore, the two dimensions CFT's energy momentum tensor is anomalous, i.e. its trace is nonzero. However, In the horizon limit the energy momentum tensor becomes holomorphic equaling the Hawking flux of the four and three dimensions black holes. This encoding of both entropy and temperature provides a uniformity in the calculation of black hole thermodynamics and statistical quantities for the non local effective action approach. We also show that the near horizon regime of a Kerr-Newman-$AdS$ ($KNAdS$) black hole, given by its two dimensional analogue a la Robinson and Wilczek, is asymptotically $AdS_2$ and dual to a one dimensional quantum conformal field theory (CFT). The $s$-wave contribution of the resulting CFT's energy-momentum-tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein-Hawking entropy via Cardy's Formula. Our derived central charge also agrees with the near extremal Kerr/CFT Correspondence in the appropriate limits. We also compute the Hawking temperature of the $KNAdS$ black hole by coupling its Robinson and Wilczek two dimensional analogue (RW2DA) to conformal matter.

Ausgehend von der Forderung, dass die Dynamik klassischer Materiefelder auf einer glatten Mannigfaltigkeit prädiktiv und quantisierbar sein muss, leiten wir einen Satz von „Mastergleichungen“ her, deren Lösungen die Dynamik (in Form einer Lagrangedichte) der den Materiegleichungen zugrundeliegenden Geometrie beschreiben. Es gelingt also das physikalische Problem der Suche nach geeigneten Gravitationsdynamiken für eine beliebige tensorielle Raumzeitgeometrie, die physikalische Materie tragen kann, in die bloß noch mathematische Frage nach der Lösung eines Systems von linearen partiellen Differentialgleichungen zu reformulieren. Dieses Ergebnis fußt auf der Einsicht, dass die Forderung nach der Prädiktivität und Quantisierbarkeit einer Materietheorie zunächst die möglichen Klassen der zugrundeliegenden Raumzeitgeometrien auf solche beschränkt, die bi-hyperbolisch sind und die Unterscheidung von positiven und negativen Energien zulassen. Gleichzeitig stellen solche Materietheorien bereits alle kinematischen Strukturen zur Verfügung, die nötig sind, um die Dynamik der Geometrie als Anfangswertproblem zu formulieren. Die Mastergleichungen stellen dann einen Ausdruck dafür dar, dass die Lagrangefunktion der Gravitationsdynamik, die die zeitliche Entwicklung von geometrischen Anfangsdaten beschreibt, eine Darstellung der Hyperflächendeformationsalgebra sein muss, welche sich ausgehend von der Dynamik der Materietheorie direkt berechnen lässt. Wir geben eine allgemeine Vorgehensweise an, mit der sich die Mastergleichungen für eine beliebige tensorielle Raumzeitgeometrie herleiten lassen und illustrieren dieses Verfahren anhand von vier physikalisch relevanten Beispielen. Die Arbeit wird abgerundet durch ein Studium von Energie-Impuls-Tensoren von Materie auf tensoriellen Raumzeiten.
Starting from classical matter dynamics on a smooth manifold that are required to be predictive and quantizable, we derive a set of `gravitational master equations'' that determine the Lagrangian describing the dynamics of the geometry on which the matter dynamics are defined. We thus convert the physical problem of finding admissible gravitational dynamics for any tensorial geometry that can support physical matter equations into the clear mathematical task of solving a system of linear partial differential equations. This result builds on the insight that predictive and quantizable matter dynamics, on the one hand, restrict the class of admissible spacetime geometries to those that are bi-hyperbolic and energy-distinguishing, and, on the other hand, provide the necessary kinematical structure needed to formulate spacetime geometry dynamics as an initial value problem. The gravitational master equations then express the fact that the Lagrangian of the gravitational dynamics must arise as a representation of the algebra of hypersurface deformations---which can be calculated from the kinematical structure imprinted on the geometry by the matter field dynamics---on a suitable geometric phase space. We provide a general prescription of how to obtain the gravitational master equations for any candidate geometry and illustrate our procedure by way of four instructive examples. We solve the master equations for metric geometry supporting Maxwell theory, finding Einstein-Hilbert dynamics as the unique solution, and for a non-trivial composite geometry supporting modified Dirac dynamics. We also discuss generalized energy-momentum tensors of matter fields and their role as sources of the gravitational dynamics obtained from the gravitational master equations.

This Thesis is devoted to the study of phenomenologically viable gravitational theories, in order to address the most pressing open issues both at very small and very large energy scales. Lovelock’s theorem singles out General Relativity as the only theory with secondorder field equations for the metric tensor. So, two possible ways to circumvent it and modify the gravitational sector are taken into account. The first route consists in giving up diffeomorphism invariance, which generically leads to extra propagating degrees of freedom. In this framework Horava gravity is discussed, presenting two restrictions, called respectively "projectability" and "detailed balance", which are imposed in order to reduce the number of terms in the full theory. We introduce a new version of the theory assuming detailed balance but not projectability, and we show that such theory is dynamically consistent as both the spin-0 and spin-2 gravitons have a well behaved dynamics at low-energy. Moreover three-dimensional rotating black hole solutions are found and fully studied in the context of Horava gravity, shedding light on its causal structure. A new concept of black hole horizon, dubbed "universal horizon", arises besides the usual event horizon one, since in Lorentz-violating gravity theories there can be modes propagating even at infinite speed. The second route which is considered, consists in adding extra fields to the gravitational action while diffeomorphism invariance is preserved. In this respect we consider the less explored option that such fields are auxiliary fields, so they do not satisfy dynamical equations but can be instead algebraically eliminated. A very general parametrization for these theories is constructed, rendering also possible to put on them very tight, theory-independent constraints. Some insight about the cosmological implications of such theories is also given. Finally in the conclusions we discuss about the future challenges that the aforementioned gravity theories have to face.

In dieser Dissertation untersuchen und entwickeln wir neue Methoden, die dabei helfen sollen eine effektive semiklassische Beschreibung der kanonischen Loop-Quantengravitation und der Spinfoam-Gravitation zu bestimmen. Einer kurzen Einführung in die Loop-Quantengravitation folgen drei Forschungsartikel, die die Resultate der Doktorarbeit präsentieren. Im ersten Artikel behandeln wir das Problem der Zeit und einen neuen Vorschlag zur Implementierung von Eigenzeit durch Randbedingungen an Pfadintegrale: wir untersuchen eine konkrete Realisierung dieses Formalismus für die freie Skalarfeldtheorie. Im zweiten Artikel übersetzen wir semiklassische Zustände der linearisierten Gravitation in Zustände der Loop-Quantengravitation. Deren Eigenschaften deuten an, wie sich Semiklassizität im Loop-Formalismus manifestiert, and wie man dies benützen könnte, um semiklassische Entwicklungen herzuleiten. Im dritten Teil schlagen wir eine neue Formulierung von Spinfoam-Modellen vor, die vollständig Triangulierungs- und Hintergrund-unabhängig ist: mit Hilfe einer Symmetrie-Bedingung identifizieren wir Spinfoam-Modelle, deren Triangulierungs-Abhängigkeit auf natürliche Weise entfernt werden kann.
In this Ph.D. thesis, we explore and develop new methods that should help in determining an effective semiclassical description of canonical loop quantum gravity and spin foam gravity. A brief introduction to loop quantum gravity is followed by three research papers that present the results of the Ph.D. project. In the first article, we deal with the problem of time and a new proposal for implementing proper time as boundary conditions in a sum over histories: we investigate a concrete realization of this formalism for free scalar field theory. In the second article, we translate semiclassical states of linearized gravity into states of loop quantum gravity. The properties of the latter indicate how semiclassicality manifests itself in the loop framework, and how this may be exploited for doing semiclassical expansions. In the third part, we propose a new formulation of spin foam models that is fully triangulation- and background-independent: by means of a symmetry condition, we identify spin foam models whose triangulation-dependence can be naturally removed.

We study the application of Bose-Einstein condensates (BECs) to simulations of phenomena across a number of disciplines in physics, using theoretical and computational methods. ¶ Collapsing condensates as created by E. Donley et al. [Nature 415, 39 (2002)] exhibit potentially useful parallels to an inflationary universe. To enable the exploitation of this analogy, we check if current quantum field theories describe collapsing condensates quantitatively, by targeting the discrepancy between experimental and theoretical values for the time to collapse. To this end, we couple the lowest order quantum field correlation functions to the condensate wavefunction, and solve the resulting Hartree-Fock-Bogoliubov equations numerically. Complementarily, we perform stochastic truncated Wigner simulations of the collapse. Both methods also allow us to study finite temperature effects. ¶ We find with neither method that quantum corrections lead to a faster collapse than is predicted by Gross-Pitaevskii theory. We conclude that the discrepancy between the experimental and theoretical values of the collapse time cannot be explained by Gaussian quantum fluctuations or finite temperature effects. Further studies are thus required before the full analogue cosmology potential of collapsing condensates can be utilised. ¶ As the next project, we find experimental parameter regimes in which stable three-dimensional Skyrmions can exist in a condensate. We show that their stability in a harmonic trap depends critically on scattering lengths, atom numbers, trap rotation and trap anisotropy. In particular, for the Rb87 |F=1,m_f=-1>, |F=2,m_f=1> hyperfine states, stability is sensitive to the scattering lengths at the 2% level. We find stable Skyrmions with slightly more than 2*10^6 atoms, which can be stabilised against drifting out of the trap by laser pinning. ¶ As a stepping stone towards Skyrmions, we propose a method for the stabilisation of a stack of parallel vortex rings in a Bose-Einstein condensate. The method makes use of a ``hollow'' laser beam containing an optical vortex, which realises an optical tunnel for the condensate. Using realistic experimental parameters, we demonstrate numerically that our method can stabilise up to 9 vortex rings. ¶ Finally, we focus on analogue gravity, further exploiting the analogy between flowing condensates and general relativistic curved space time. We compare several realistic setups, investigating their suitability for the observation of analogue Hawking radiation. We link our proposal of stable ring flows to analogue gravity, by studying supersonic flows in the optical tunnel. We show that long-living immobile condensate solitons generated in the tunnel exhibit sonic horizons, and discuss whether these could be employed to study extreme cases in analogue gravity. ¶ Beyond these, our survey indicates that for conventional analogue Hawking radiation, simple outflow from a condensate reservoir, in effectively one dimension, has the best properties. We show with three dimensional simulations that stable sonic horizons exist under realistic conditions. However, we highlight that three-body losses impose limitations on the achievable analogue Hawking temperatures. These limitations vary between the atomic species and favour light atoms. ¶ Our results indicate that Bose-Einstein condensates will soon be useful for interdisciplinary studies by analogy, but also show that the experiments will be challenging.

This thesis focusses on three main aspects of the foundations of any theory of gravity where the gravitational field admits a geometric interpretation: (a) the principles of equivalence; (b) their role as selection rules in the landscape of extended theories of gravity; and (c) the possible modifications of the spacetime structure at a "mesoscopic" scale, due to underlying, microscopic-level, quantum-gravitational effects. The first result of the work is the introduction of a formal definition of the Gravitational Weak Equivalence Principle, which expresses the universality of free fall of test objects with non-negligible self-gravity, in a matter-free environment. This principle extends the Galilean universality of free-fall world-lines for test bodies with negligible self-gravity (Weak Equivalence Principle). Second, we use the Gravitational Weak Equivalence Principle to build a sieve for some classes of extended theories of gravity, to rule out all models yielding non-universal free-fall motion for self-gravitating test bodies. When applied to metric theories of gravity in four spacetime dimensions, the method singles out General Relativity (both with and without the cosmological constant term), whereas in higher-dimensional scenarios the whole class of Lanczos--Lovelock gravity theories also passes the test. Finally, we focus on the traditional, manifold-based model of spacetime, and on how it could be modified, at a "mesoscopic" (experimentally attainable) level, by the presence of an underlying, sub-Planckian quantum regime. The possible modifications are examined in terms of their consequences on the hypotheses at the basis of von Ignatowski's derivation of the Lorentz transformations. It results that either such modifications affect sectors already tightly constrained (e.g. violations of the principle of relativity and/or of spatial isotropy), or they demand a radical breakdown of the operative interpretation of the coordinates as readings of clocks and rods.

String theory imposes slight modifications to Einstein's equations of general relativity (GR). In (4), the authors claim that the gravitational field equations in empty space, which in GR are just R [subscript greek letters mu nu ] = 0, should hold one extra term which is first order in the string constant [alpha'] and proportional to the Riemann curvature tensor squared. They do admit, however, that this simple modification is just schematic. In (1) the authors use modified equations which are coupled to the dilation field. We show that equations given in (4) do not admit an isotropic solution; justification of these equations would require sacrificing isotropy. We thus investigate the consequences of the coupled equations from (1) and the black-hole solution they give there. We calculate the additional perihelion precession of Mercury, the added deflection of photons by the sun, and the extra gravitational redshift which should be present if these equations hold. We determine that additional effects due to string theory in each of these cases are quite minuscule.
B.S.
Bachelors
Sciences
Physics

Doutoramento em MAP-Fis
This thesis presents recent studies on test scalar and vector fields around black holes in the classical theory of General Relativity. It is separated in two parts according to the asymptotic properties of the spacetime under study. In the first part, we investigate scalar and Proca fields on an asymptotically flat background. For the Proca field, we obtain a complete set of equations of motion in higher dimensional spherically symmetric backgrounds. These equations are solved numerically, both to compute Hawking radiation spectra and quasi-bound states. In the former case, for the first time, we carry out a precise study of the longitudinal degrees of freedom induced by the mass of the field. This can be used to improve the modeling of evaporation of black holes coupled to massive vector fields, and black hole event generators currently used at the Large Hadron Collider to probe TeV gravity models with extra dimensions. Regarding quasi-bound states, we find arbitrarily long lived modes for a charged Proca field in a Reissner-Nordström black hole. As a comparison, we also find such long lived modes for a charged scalar field. The second part of this thesis presents research on superradiant instabilities of scalar and Maxwell fields on an asymptotically anti-de Sitter background. For the scalar case, we introduce a charge coupling between the field and the background, and show that superradiant instabilities do exist for all values of the total angular momentum, `, in higher dimensions. This result corrects a statement in the literature that such instabilities only appear in even dimensions. For the Maxwell case, we first propose a general prescription to impose boundary conditions on the Kerr-anti-de Sitter spacetime, and obtain two Robin boundary conditions which give two different quasinormal modes even in a simpler Schwarzschild-anti-de Sitter black hole. Then these two boundary conditions are implemented to study superradiant unstable modes and vector clouds. In particular, we find that the new branch of quasinormal modes may be unstable in a larger parameter space. Furthermore, the existence of vector clouds indicates that one may find a vector hairy black hole solution for the Einstein-Maxwell-anti-de Sitter system at the nonlinear level, which implies, in such system, that the Kerr-Newman-anti-de Sitter black hole is not a unique solution.
Nesta tese apresentamos estudos recentes sobre campos escalares e vetoriais de teste, em torno de buracos negros na teoria clássica da relatividade geral. A tese encontra-se dividida em duas partes, de acordo com as propriedades asimtóticas do espaço-tempo em estudo. Na primeira parte, investigamos os campos escalar e de Proca num espaço asimtóticamente plano. Para o campo de Proca, obtemos um conjunto completo de equações do movimento em espaços esfericamente simétricos em dimensões elevadas. Estas equações são resolvidas numericamente, tanto para o cálculo de radiação de Hawking como para o cálculo de estados quasi-ligados. No primeiro cálculo, pela primeira vez, efetuamos um estudo preciso dos graus de liberdade longitudinais que são induzidos pelo termo de massa do campo. Este estudo pode ser usado para melhorar o modelo da evaporação de buracos negros acoplados a campos vetoriais massivos e geradores de eventos de buraco negro usados presentemente no Grande Colisor de Hádrons para testar modelos de gravidade com dimensões extra à escala do TeV. Relativamente aos estados quasi-ligados, encontramos estados com tempos de vida arbitrariamente longos para o campo de Proca carregado, no buraco negro de Reissner-Nordström. Como comparação, obtemos estados com tempos de vida arbitrariamente longos também para o campo escalar. Na segunda parte da tese, apresentamos investigação sobre instabilidades super-radiantes para os campos escalar e de Maxwell em espaço asimtóticamente anti-de Sitter. No caso escalar introduzimos um acoplamento de carga entre o campo e o background e mostramos que instabilidades super-radiantes existem para todos os valores do momento angular total, `, em dimensões mais elevadas. Este resultado corrige a afirmação na literatura de que estas instabilidades aparecem apenas em dimensões ímpares. Para o caso do campo de Maxwell, propomos primeiro uma prescrição para impor condições fronteira no espaço tempo de Kerr-antide Sitter obtendo duas condições fronteira do tipo de Robin que originam dois tipos diferentes de modos quasi-normais, mesmo no caso mais simples do buraco negro de Schwarzschild-anti-de Sitter. Estas duas condições fronteira são implementadas no estudo de modos super-radiantes instáveis e nuvens vetoriais. Em particular, encontramos um novo ramo de modos quasi-normais que podem conter instabilidades mais fortes. Mostramos ainda que a existência de nuvens vetoriais indica a possível existência de soluções de buraco negro com cabelo vetorial para o sistema Einstein-Maxwell-anti-de Sitter a nível não linear, o que implica, nesse sistema, que o buraco negro de Kerr-Newman-anti-de Sitter poderá não ser único.

For ninety years we have known that our universe is in expansion. Cosmological data favor an unknown form of intrinsic and fundamental uniform energy contributing approximately 68% of the total energy budget in the current epoch. The simplest proposal in accordance with observations is the standard cosmological model consisting of a small but positive cosmological constant producing a gravitational repulsive effect driving the accelerated expansion. In standard cosmology general relativity is assumed as the theory for gravity, which in turn predicts that a sufficiently compact mass can deform spacetime and form a black hole. At a mathematical level, these objects are considered vacuum solutions described by very few parameters. For instance, a stationary black hole solution is completely described by its mass, angular momentum, and electric charge; and two black holes that share the same values for these parameters, are indistinguishable from one another. On the basis of the usual metrics describing black holes, it is generally believed that all contained matter is localized in the center or, if rotating, on an infinitely thin ring. Recent approaches challenge this unintuitive assumption and consider matter just spread throughout the interior. Clearly, this begs for a quantum description in curved space. In past years, a novel approach established a new bridge between quantum information and the physics of black holes when an intriguing proposal was made: black holes could possibly be understood as Bose—Einstein condensates of soft interacting but densely packed gravitons. The aim of this thesis is to discuss how to construct a graviton condensate structure on top of a classical gravitational field describing black holes. A necessary parameter to be introduced for this analogy is a chemical potential which we discuss how to incorporate within general relativity. Next we search for solutions and, employing some very plausible assumptions, we find out that the condensate vanishes outside the horizon but is non-zero in its interior. These results can be extended easily to a Reissner—Nordström black hole. In fact, we find that the phenomenon seems to be rather generic and is associated with the presence of a horizon, acting as a confining potential. In order to see whether a Bose— Einstein condensate is preferred, we use the Brown—York quasilocal energy, finding that a condensate is energetically favourable in all cases in the classically forbidden region. The Brown—York quasilocal energy also allows us to derive a quasilocal potential, whose consequences allow us to suggest a possible mechanism to generate a graviton condensate in black holes. On the contrary, this is not the case for any kind of horizons; for instance, this mechanism appears not to be feasible in order to generate a quantum condensate behind the cosmological de Sitter horizon. Furthermore, when a pair of black holes merge, an immense amount of energy should be given off as gravitational waves. Their wave forms have been recently confirmed to be perfectly described by general relativity. We discuss why for low frequency gravitational waves aimed to be detected by astrophysical PTA observations the fact that propagation should take place over an expanding (approximately globally de Sitter) spacetime should be taken into account. In this manner, harmonic waves produced in such mergers would become anharmonic when measured by cosmological observers. This effect is tiny but appears to be observable for gravitational waves to which PTA are sensitive. Therefore we have characterized modifications to the expected signal, and how it is related to the source and pulsar characteristics that are employed by the IPTA collaboration. If the cosmological constant were an intrinsic property, this experiment would be capable of confirming the relevance of lambda at redshift z < 1.
El objetivo de la presente tesis es profundizar en diversos aspectos de la física de los agujeros negros. Tanto en lo que respecta a sus características constitutivas fundamentales, su "estructura" interna, como a la posibilidad de observar o detectar mediante observaciones astrofísicas ciertos efectos producto de su dinámica. Por un lado, hemos seguido las ideas de Dvali, Gómez et al. quienes han sugerido la posibilidad de que un agujero negro sea un condensado de Bose—Einstein de gravitones débilmente interactuantes. En nuestro caso hemos estudiado la existencia de este tipo de soluciones sobre diferentes métricas de agujero negro (Schwarzschild y Reissner— Nordström) que actuarían como potencial confinante para dichos condensados. Un parámetro necesario para ello, es el equivalente a un potencial químico que debe ser incorporado a la relatividad general. Cabe destacar que la solución encontrada puede ser interpretada como la función de campo medio del condensado. Además resulta fuertemente ligada a la estructura clásica de la métrica que la sustenta. Por otro lado, es bien sabido que la aceleración de cuerpos muy masivos producen perturbaciones de tipo onda en el espaciotiempo. Son de nuestro interés las ondas gravitatorias de baja frecuencia, provenientes de la colisión de agujeros negros supermasivos y que deberían poder ser detectadas mediante sistemas de púlsares (Pulsar Timing Arrays). De acuerdo a una línea de investigación desarrollada por Espriu et al. la presencian de una constante cosmológica podría tener un efecto en la propagación y por lo tanto en la detección por parte de la colaboración IPTA de estas ondas. En la presente tesis hemos generalizado el método para incluir diferentes tipos de materia (relativista y no relativista) además de la constante cosmológica. Del análisis se deriva que el efecto depende sensiblemente del valor de la constante de Hubble (que engloba todos los tipos de materia presentes). Continuando dicha línea, hemos caracterizado detalladamente el efecto en su dependencia con los parámetros cosmológicas y las distancias involucradas, y cómo podría ser hallado. Esperamos que nuestros resultados puedan contribuir a una definitiva detección por IPTA.

The goal of this thesis is to obtain and study new black hole solutions, both with and without supersymmetry, with a particular focus on multi-centered black holes in a cosmological background. After a review of matter-coupled N=2 gauged supergravity in four dimensions and of the classification of its supersymmetric solutions, a new supersymmetric black hole solution is obtained, which is the first with nontrivial running hyperscalars. Fake supergravity is a framework that allows to apply the methods used to classify supersymmetric solutions of supergravity also to theories without supersymmetry. A classification of fake supersymmetric solutions of a theory related to N=2, d=4 gauged supergravity is reviewed and used to construct dynamical solutions representing multiple black holes in a Friedmann-Lemaître-Robertson-Walker background. The physical properties of the single-centered case are then studied in some detail. More complicated solutions with rotation and NUT-charge, or with curved spatial slices, are obtained for a less general class of theories. Finally a recipe to obtain multi-centered black holes in an arbitrary FLRW universe and in arbitrary dimension is presented. These spacetimes are a multi-centered generalization of the charged McVittie black hole and are sourced by a U(1) gauge field and by a charged perfect fluid. As a particular subcase, these solutions describe an arbitrary number of black holes in a background that is locally anti-de Sitter space in cosmological coordinates. Some physical properties of the single-centered asymptotically AdS black hole are studied, showing in particular that a generalized first law of black hole dynamics is satisfied.

O objetivo deste trabalho é a obtenção numérica de soluções periódicas para o problema geral de N corpos sujeitos apenas à atração gravitacional mútua. Em particular, procuramos soluções chamadas de coreografias, que apresentam em comum a propriedade de que todos os corpos se movem sobre a mesma curva. O interesse neste tipo de solução aumentou muito recentemente devido aos avanços na Física das ondas gravitacionais. Com a possível detecção de ondas gravitacionais prevista para um futuro próximo, todas as configurações periódicas do problema de N corpos passam a ser consideradas como possíveis fontes de radiação gravitacional. Identificar os padrões de radiação associados a estas órbitas é uma das tarefas prementes atualmente na área. Tendo isso em vista, iremos calcular também as ondas gravitacionais emitidas por um sistema em que os corpos que o constituem seguem uma órbita coreográfica. Começamos este trabalho com um capítulo que descreve historicamente a busca pela solução geral do problema de N corpos, inicialmente motivada pelo interesse na análise da estabilidade do Sistema Solar. Em seguida, no Capítulo 2, apresentamos as principais definições e teoremas que serão utilizados ao longo do texto. O leitor pode escolher entre seguir este capítulo no início de sua leitura, ou então utilizá-lo para consulta quando necessário. No Capítulo 3, identificamos os graus de liberdade do sistema formado pelos N corpos e determinamos quais grandezas físicas nele se conservam, através do Teorema de Noether. Com isso estabelecemos a não integrabilidade deste sistema, no sentido de Liouville, para N > 2. Escrevemos também a solução geral do problema de dois corpos, conhecido como problema de Kepler, e mostramos duas soluções particulares para o problema de três corpos com massas iguais, conhecidas como soluções de Euler (1765) e Lagrange (1772). Na solução de Euler, os três corpos estão dispostos sobre uma mesma reta que gira com velocidade angular constante ao redor do seu centro de massa, e na de Lagrange, estão dispostos sobre os vértices de um triângulo equilátero que gira com velocidade angular constante ao redor do seu centro de massa. Com o intuito de descrever as soluções periódicas conhecidas para o Problema de N Corpos, no Capítulo 4 estudaremos as órbitas homográficas, que apresentam a característica de que a configuração do sistema em qualquer instante pode ser obtida através de uma rotação composta com uma dilatação/contração da configuração inicial. Essas soluções generalizam as soluções de Euler e Lagrange citadas anteriormente. No Capítulo 5, analisaremos as órbitas coreográficas. Esta classe de soluções foi descoberta por Cris Moore em 1993, que encontrou numericamente uma solução coreográfica para o problema de três corpos em que eles seguem uma mesma curva em forma de oito. A existência e a estabilidade desta solução foram estudadas de maneira rigorosa por Richard Montgomery e Alain Chenciner. Neste trabalho, damos um esboço de como construir a solução em forma de oito no caso em que as massas são idênticas. Simularemos esta e outras órbitas coreográficas, além de algumas outras órbitas periódicas descritas anteriormente, através do método de integração de Runge-Kutta de quarta ordem. Finalmente, no Capítulo 6 calculamos as ondas gravitacionais emitidas pelas órbitas homográficas e coreográficas simuladas anteriormente. Finalizaremos com uma breve discussão comparando os padrões de ondas gravitacionais obtidos para as diferentes órbitas e analisando a possibilidade de determinar a fonte de emissão a partir da medida de um sinal de uma onda gravitacional.
The purpose of this work is the numerical computing of the periodic solutions to the N-body problem, that is, the general problem of determinig the motion of N bodies exclusively subject to gravitational forces between them. In particular, we search for solutions that were named choreographies, which have in common the property that all bodies move along the same curve. The interest in this kind of solution has recently increased due to technological advances in Gravitational Wave (GW) Physics. As the detection of Gws is foreseen for the near future, all periodic configurations of the N-body problem may be considered as possible sources of gravitational radiation. Identifying the patterns of radiation associated to these orbits is nowadays one of the pressing tasks in this field. Having this fact in mind, we calculate the GWs emitted by a system in which all bodies describe a choreographic orbit. In Chapter 1, we briefly describe the history of the search for the general solution to the N-body Problem, initially motivated by the interest in the stability analysis of the Solar System. Next, in Chapter 2, we present the main definitions and theorems to which we refer during this text. The reader may opt between following this chapter as he begins to read this thesis and consulting it only if necessary or when he is referred to. In Chapter 3, we identify the degrees of freedom of the system consisting of N bodies and determine the physical quantities it conserves, through Noethers theorem. Doing that, we establish the non-integrability of our dynamical system, in the sense of Liouville integrability, if N > 2. We also give the general solution to the 2-body problem, known as Keplers Problem, and present two particular solutions to the 3-body Problem, known as Eulers solution (1765) and Lagranges solution (1772). In Eulers solution, all three bodies are in the same line, which revolves around its center of mass, and in Lagranges solux tion they are at the vertices of an equilateral triangle, which also revolves around its center of mass. In order to describe all known periodic solutions to the N-body Problem, in Chapter 4 we study homographic orbits, that is, orbits in which the configuration at any instant can be obtained by a rotation and a dilation/contraction of the initial configuration. These solutions generalize the solutions by Euler and Lagrange mentioned above. In Chapter 5, we analyze choreographic orbits. This class of solutions was discovered by Cris Moore in 1993, who computed numerically a choreographic solution in which the bodies move along the same curve in the shape of an eight. The existence and stability of this orbit were rigorously studied by Richard Montgomery and Alain Chenciner. Here, we sketch the construction of the figure eight solution in the particular case where all masses are identical. We simulate this and other choreographic solutions, as well as some other periodic solutions described before, through the use of a fourth order Runge- Kutta method of numerical integration. Finally, in Chapter 6 we calculate the Gws emitted by the homographic and choreographic orbits simulated before. We end this work with a brief discussion comparing the GW patterns obtained to different orbits and analyzing the possibility of determining the mission source from a measurement of a GW signal.

Mes travaux de thèse portent sur le développement d’un capteur inertiel à atomes froids à portée métrologique de nouvelle génération. Son architecture est basée sur deux sources atomiques indépendantes interrogées simultanément par une séquence d’interférométrie atomique commune aux deux sources. Aussi, dans l’optique d’atteindre des performances de mesure ultimes, notre instrument repose sur des fonctions optiques de manipulation d’atomes froids de dernières générations: oscillations de Bloch et séparatrices multi-photoniques. En trois ans, notre instrument a atteint un niveau de développement suffisant pour faire la démonstration de son principe de fonctionnement, permettant de mesurer simultanément l’accélération de la pesanteur g et son gradient vertical. En particulier, nous avons démontré une nouvelle méthode de mesure qui permet de s’affranchir non seulement des bruits en mode commun, mais aussi des fluctuations de la ligne de base de l’instrument, pour la détermination du gradient de gravité. Pour mener à bien ces travaux, j’ai également utilisé un prototype de banc optique industriel pour application spatiale, développé dans le cadre d’un projet financé par l’Agence Spatiale Européenne (ESA) et coordonné par la société Muquans. En parallèle des développements sur notre instrument, nous avons testé et caractérisé ce banc fibré qui réalise toutes les fonctions optiques nécessaires au fonctionnement d’un interféromètre atomique dans l’espace
This work focuses on the development of a new generation of cold-atom inertial sensor. Its architecture is based on two independent atomic sources simultaneously interrogated by an interferometric sequence common to both sources. In addition, in order to achieve ultimate measurement performance, our instrument is based on the latest optical methods for atomic manipulation: Bloch oscillations and multi-photon transitions. During my thesis, the instrument has reached a level of development to perform a proof-of-principle operation, allowing to simultaneously measure the gravity acceleration g and its vertical gradient. In particular, we demonstrated a new measurement method that allows to overcome not only common mode noise, but also the baseline fluctuations of the instrument, for the determination of the gravity gradient. To carry out this work, I also used a prototype of industrial optical bench for space application, developed as part of a project funded by the European Space Agency (ESA) and coordinated by the Muquans company. In parallel with the developments of our instrument, we tested and characterized this fiber bench which fulfills all the optical functionalities necessary for the operation of an atom interferometer in space

Uppsatsens syfte ligger i att undersöka huruvida filmteoretikern David Bordwells två inflytelserika berättarmodeller från 1980-talet fortfarande återfinns inom samtida filmproduktion. Jag fördjupar mig i det klassiska- respektive konstfilmsberättandet och jämför vidare de typiska elementen från de två berättarmodellerna med formatet slow cinema. I definitionen av slow cinema utgår jag ifrån filmvetaren Matthew Flanagans utredning av vad formatet innebär samt de tre byggstenarna han anser vara mest väsentliga. Dessa är långa tagningar, en ickeberättande struktur och skildringar av realistiska, vardagliga skeenden. Med en utgångspunkt i detta utför jag en närläsning av Alfonso Cuaróns film Gravity (2013). Analysen fokuserar på hur element från slow cinema kan adapteras till en mer kommersiellt accepterad film med ett klassiskt berättande. Gravity visar sig exemplifiera dels Cuaróns personliga stil men även ett samspel av element från de två berättarmodellerna, och slow cinema. Avslutningsvis förs en diskussion där jag jämför analysens resultat dels med tidigare forskning samt ett antal andra filmexempel. Slutsatsen blir således att konstnärlig auktoritet och filmisk kvalitet likväl kan uppstå inom kommersiella modeller som konstnärliga sådana. Dagens filmklimat och dess vidare utveckling kan gynnas av en uppluckring av de föråldrade konventioner som Bordwells berättarmodeller innebär. Istället skall filmskapare fritt kunna röra sig mellan olika stilar, tillvägagångsätt och berättande, likt Cuaróns förkroppsligade kamera.

In this thesis, I demonstrate the dynamic way in which musical processes can be described as metaphors. Using Steve Larson’s three main metaphors (gravity, inertia, and magnetism) as a starting point, I propose additional metaphors (friction, repulsion, momentum, wave, orbit, and oscillation) to analyze the first movements of Mozart’s Piano Concerto No. 20 in D minor, K 466 and Schumann’s Piano Concerto in A minor, op. 54. These metaphors provide a means to discuss points of convergence and divergence between the Classical style and the early-Romantic style. Additionally, most theorists of the energeticist tradition only discuss motion through prose; I introduce a way to represent these metaphors as musical examples. By focusing on the listener’s experience through musical motion, the model proposed in this thesis is useful, not only for the theorist, but for all who wish to communicate ideas about music in a dynamic way.

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The subject of Classic Gravitation is part of the actual curriculum for High School in Brazil, and it is taught in the first year of that education level. This master thesis presents a research regarding the subject Classic Gravitation in High School. This research was based in two complementary guidelines of research and action. The first guideline was the analysis of 21 didactic books of physics which are the more frequently used in High School, in the city of Natal/RN. The second guideline, worked after being verified the most common deficiencies presents in the didactic books, was the elaboration, followed by a practical application, of a course suggesting how to approach that subject in the classroom. The Par?metros Curriculares Nacionais para o Ensino M?dio (National Curricular Parameters for High School PCNEM) defend that Classic Gravitation is very important in the student s formation and that its study helps the comprehension of many nature s phenomena. Because of this vision of that subject by the PCNEM, the 21 analyzed books were separated in two groups: the first one, containing 10 books, was edited before the spreading of PCNEM, and the second, with 11 books, after that spreading. Whatever the group to which the didactic books belonged, the great majority of them let that subject in a second plan; two of them even suggesting, in the teacher s orientations, that the subject Gravitation can be suppressed in case of insufficient time . These analyses points that the PCNEM had produced no changes in the conception of the authors that wrote books regarding that subject. To analyze the didactic books, we elaborated a script which was used as an analysis tool, in which we put in evidence the relative importance of the historic and philosophic contextualization of the subject, the quotidian experience of the students and the interdisciplinary approach, among other aspects. It became evident that the didactic books give very little emphasis to historic aspects of the knowledge construction, to the relations with the day-by-day questions and to the interdisciplinary character of the subject Gravitation. It calls attention the non concordance among the authors opinions regarding the necessary previous knowledge or prerequisites the students should fulfill in order to begin to study Gravitation. The course we elaborated was given to a group of teachers as well as to students. In those courses we treated theoretical and practical aspects and emphasized historical questions and the ones which are related to people s daily life. The course for teachers was realized as an extra-mural activity of the UFRN and was given by the author of this thesis at the Escola Estadual Francisco Ivo Cavalcanti (a state public school in Natal/RN). There were 23 teachers present, from several public schools and several fields of knowledge. The thesis supervisor and the master degree s colleagues of the author acted as collaborators , reporting the participants opinions and speeches. The course to the students, on the other hand, had the participation of 300 regular students who belonged to 6 different 1st year classes of the High School Escola Marista de Natal (RN), in which the author acts as a physics teacher. The student s course was realized as part of the regular curriculum activities, in which three classes stood under the responsibility of the author and other three classes in charge of another Marista s teacher, who participated as a collaborator . The teacher s course as well as the students one were given in two stages, with five hours each. The first stage was divided in two moments, the first one focused on the survey of the spontaneous conceptions about gravitation, in which we worked basically with experiments of free throwing and pendulum, and the second one focused in theoretical presentations and quarrels about universe s models. In the second stage of the course we improved the study of Kepler s laws and the Newton s Universal Gravitation law, and we used as motivating tools some practices involving the construction of the solar system in scale. As instruments for evaluating both courses we used questionnaires and reported the speeches with participants opinions, beyond usual written evaluations in the course for the students. The teachers who participated in the course showed very good wills in realizing interdisciplinary practices; nevertheless, according their own speeches, they frequently came across the difficulty of how to do . From the experience we had in both courses, we conclude that the approach we propose hear to the teaching of the subject Classic Gravitation , supported on the tripod theory, practice and historical and philosophical aspects, is viable and effective. One hopes that this research may contribute in the formation of a opinion, among the teachers, concerning how to approach the subject of Classic Gravitation, and may offer suggestions in order those who want to apply that approach may develop classroom practices aiming to improve the teaching of that subject, which has a singular importance in the formation of High School students
O tema Gravita??o Cl?ssica faz parte do curr?culo vigente para o Ensino M?dio, sendo ministrado na 1a s?rie desse n?vel de ensino. Esta disserta??o apresenta uma pesquisa a respeito do tema Gravita??o Cl?ssica no Ensino M?dio baseada em dois eixos norteadores e complementares de pesquisa e a??o. O primeiro eixo ap?ia-se na an?lise de 21 livros did?ticos de F?sica, que s?o mais comumente utilizados no Ensino M?dio na cidade de Natal/RN. O segundo eixo, trabalhado ap?s serem verificadas as defici?ncias mais comuns presentes nos livros did?ticos, corresponde ? elabora??o, seguida da aplica??o pr?tica, de um curso sugerindo como abordar o tema em sala de aula. Os Par?metros Curriculares Nacionais para o Ensino M?dio (PCNEM) advogam que esse tema ? muito importante para a forma??o dos alunos e que o seu estudo auxilia na compreens?o de diversos fen?menos da natureza. Considerando essa vis?o do tema pelos PCNEM, os 21 livros analisados foram separados em dois grupos: o primeiro grupo, com 10 livros, foi editado antes da divulga??o dos PCNEM, e o segundo grupo, com 11 livros, ap?s a sua divulga??o. Independentemente de pertencer ao primeiro ou ao segundo grupo, a grande maioria dos livros did?ticos relega o tema para um segundo plano; dois deles chegam ao extremo de sugerir, nas orienta??es aos professores, que o conte?do Gravita??o seja omitido, caso o tempo seja insuficiente . Essa constata??o sinaliza no sentido de que os PCNEM n?o produziram nenhuma mudan?a na concep??o dos autores dos livros a respeito do tema. Para a an?lise dos livros did?ticos, utilizou-se como instrumento um roteiro que elaboramos, por meio do qual se procurou evidenciar a import?ncia relativa da contextualiza??o hist?rica e filos?fica do tema, da experi?ncia cotidiana dos alunos e da interdisciplinaridade, entre outros pontos. Constatou-se que os livros did?ticos pouco enfatizam os aspectos hist?ricos da constru??o do conhecimento, a rela??o com as quest?es do cotidiano e o car?ter interdisciplinar do tema Gravita??o. Chama a aten??o a n?o concord?ncia entre os autores a respeito do conhecimento anterior ou dos pr?-requisitos necess?rios aos alunos para iniciarem o estudo da Gravita??o. O curso que elaboramos foi ministrado tanto para professores como para alunos, sendo abordados aspectos te?ricos e pr?ticos, com ?nfase em quest?es hist?ricas e em quest?es relacionadas com o cotidiano das pessoas. O curso para professores foi realizado como uma atividade de extens?o da UFRN e foi ministrado, pela autora desta disserta??o, na Escola Estadual Francisco Ivo Cavalcanti (Natal/RN). Fizeram-se presentes a esse evento 23 professores de v?rias escolas da rede p?blica e de v?rias ?reas do conhecimento. O orientador e os colegas mestrandos da autora desta disserta??o atuaram como colaboradores, registrando opini?es e relatos dos participantes. O curso para alunos contou com a participa??o de 300 alunos regularmente matriculados em seis diferentes turmas do 1? ano do Ensino M?dio da Escola Marista de Natal/RN, onde a autora desta disserta??o atua como professora de F?sica. Esse curso para alunos foi realizado como parte das atividades curriculares normais, ficando tr?s turmas sob responsabilidade direta da autora desta disserta??o e tr?s outras a cargo de outro professor da escola, que atuou como colaborador. Tanto o curso para professores como o curso para alunos constou de duas etapas, cada uma de 5 horas. A primeira etapa foi desdobrada em dois momentos, sendo o primeiro centrado no levantamento das concep??es espont?neas sobre Gravita??o, trabalhando-se basicamente com os experimentos de lan?amento livre e p?ndulo; o segundo momento centrou-se em apresenta??es te?ricas e discuss?es sobre os modelos de universo. A segunda etapa do curso foi um aprofundamento sobre as Leis de Kepler e a Lei da Gravita??o Universal de Newton, sendo utilizadas, como instrumentos motivadores, pr?ticas envolvendo constru??es do sistema solar em escala. Como instrumentos de avalia??o de ambos os cursos, foram utilizados question?rios e relatos de opini?es, al?m de avalia??es usuais, na vers?o do curso para alunos. Os professores participantes demonstraram disponibilidade para realizar pr?ticas interdisciplinares; todavia, segundo seus pr?prios relatos, eles freq?entemente esbarravam na dificuldade do como fazer . Da experi?ncia vivida nos dois cursos, verificou-se que a abordagem aqui proposta para o tema Gravita??o Cl?ssica, apoiada no trip? teoria, pr?tica e aspectos hist?ricos e filos?ficos, ? vi?vel e efetiva. Espera-se que essa pesquisa possa contribuir na forma??o de uma opini?o, entre os professores, a respeito de como abordar o tema Gravita??o Cl?ssica, e possa fornecer subs?dios para que os interessados desenvolvam pr?ticas em sala de aula visando aprimorar o ensino desse tema, que ? de import?ncia ?mpar na forma??o dos alunos do Ensino M?dio

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
A formulaÃÃo e comprovaÃÃo experimental de uma teoria consistente de GravitaÃÃo QuÃntica à um dos maiores desafios da FÃsica atualmente. Entre as candidatas a ocupar este posto està a GravitaÃÃo QuÃntica de LaÃo, ela sugere a reinterpretaÃÃo do espaÃo-tempo que, em escala planckiana, assume a forma de uma rede de pontos espaÃados por um comprimento mÃnimo caracterÃstico da natureza. Neste trabalho tratamos de um modelo recentemente introduzido que incorpora o conceito de comprimento mÃnimo e o aplica no contexto de baixas energias, a MecÃnica QuÃntica PolimÃrica, discutimos a diferenÃa entre a fÃsica deste modelo e dos modelos de incerteza mÃnima, em especial o PrincÃpio de Incerteza Generalizado, onde a discretizaÃÃo espacial e consequÃncia de alteraÃÃes nas relaÃÃes de comutaÃÃo canÃnicas. Usamos o mÃtodo perturbativo para calcular correÃÃes de primeira ordem nos espectros de energia de alguns potenciais conhecidos, observamos atravÃs de grÃficos as escalas de energia envolvidas e comparamos os resultados com outras correÃÃes que surgem no contexto de altas energias.
The formulation and experimental verication of a consistent theory of Quantum Gravitation is one of the greatest challenges in Physics nowadays. Between the candidates for this post is the Loop Quantum Gravity, it suggests a reinterpretation of space-time, that in planckian scale, would assume the form of a net of points spaced by a minimal length characteristic of nature. In this work we deal with a model that incorporates this concept and applies it to the context of low energies, the Polymer Quantum Mechanics, we discuss the dierences on the physics of this model an that of the model on minimal uncertainty, in special the Generalized Uncertainty principle, where the spacial discretization is a consequence of modications in canonical commutation relations. We use the perturbative method to calculate rst order corrections in the energy spectra of some known potentials, we observe through graphics the energy scales involved and compare the results with other corrections that arise in the context of high energies.

博士
國立臺灣大學
物理學研究所
104
We discuss the boundary effect of anomaly-induced action in 2-dimensional and 4-dimensional spacetime, which is ignored in previous studies. Anomalyinduced action, which gives the stress tensor with the same trace as the trace anomaly, can be represented in terms of local operators by introducing an auxiliary scalar field. Although the degrees of freedom of the auxiliary field can in principle describe the quantum states of the original field, the correspondence between them was unclear. We show that, by considering the boundary effect, the missing correspondence will be restored. Therefore, from now on, this technique has become a mature and independent tool to calculate the renormalized stress tensor in curved spacetime. Also, we find that the anomaly-induced action can only be used for the spacetime with zero Euler characteristic which is in general not true in 4-dimension. As examples, we demonstrate our formalism via several different spacetime and famous quantum gravity issues to show how efficient and powerful this approach is. We expect that our new formalism can become an useful tool to study various interesting quantum gravity effects. This thesis is based on the works [1, 2]. [1] is already published and [2] is about to be submitted for publication.

In this Ph.D. thesis we analyse both classical and quantum effects relevant for the study of cosmological perturbations. We choose this particular topic because, through the analysis of cosmological perturbations, it is possible to explore a wide range of different physical phenomena. Moreover, they are a central and important piece in the puzzle of the history of the universe. The most obvious relevance of cosmological perturbations is the study of structure formation and the large scale structure of the universe. In this regard, such perturbations are related to primordial gravitational waves and primordial magnetic fields. Given their dependence on pre-recombination phenomena, they could give us some information on the universe before hydrogen recombination. Classical perturbations have been widely studied in literature, with the main focus on isotropic cosmological models. While this is usually a good approximation, the presence of a primordial magnetic field causes a coupling between different algebraic modes of the usual decomposition, connecting density perturbations, primordial magnetic fields and primordial gravitational waves. Moreover, the presence of the magnetic field requires the use of an anisotropic cosmological model. While small, these relations are important in the evolution of anisotropic structures. Furthermore, such primordial seeds of the magnetic fields are widely believed to be the origin of the magnetic fields measured today in galaxies. In the first part of this thesis, we analyse these relations, together with the possible effects that a non ideal, i.e. viscous, cosmological fluid could have on the growth of perturbations. We focus our attention to a Bianchi I model, improving the results of some preceding papers. The second part of the thesis focuses on the semiclassical approximation of quantum gravity. Quantum effects are believed to influence the birth and dynamics of perturbation seeds and, in general, the dynamics of the primordial universe. This way, the mathematical scheme used to represent these effects is a central point in the description of quantum gravity regarding such seeds. Furthermore, even more care is required to split the WKB action between embedding variables and physical degrees of freedom, and in many models the quantum gravity corrections to the Schrödinger equation violate the unitarity of the system evolution. This decomposition shares some similarities with the Born-Oppenheimer approximation of molecular physics. We perform a critical analysis of two different ways to apply this decomposition. In particular, we analyse limits and perspectives of the different proposals to solve the non unitarity problem, even comparing expansions in different fundamental physical constants (Planck constant and mass). We find the source of non-unitary effects in a common assumption in the definition of WKB time, and we propose an alternative formulation. Also, we show how the usual assumptions of classicality of the physical quantities must be handled with care, focusing our attention to the implementation of the classical background in the perturbation scheme. Studies in this research field are very important because they could bind CMB measurements and primordial gravitational waves to quantum gravity, bringing us finally an experimental playground.

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.