Dissertations / Theses on the topic 'Relativity and gravitational theory – General relativity – Black holes'

General relativity (GR) has stood as the most accurate description of gravity for the last 100 years, weathering a barrage of rigorous tests. However, attempts to derive GR from a more fundamental theory or to capture further physical principles at high energies has led to a vast number of alternative gravity theories. The individual examination of each gravity theory is infeasible and as such a systematic method of examining modified gravity theories is a necessity. Studying generic classes of gravity theories allows for general statements about observables to be made independent of explicit models. Take, for example, those models described by the Horndeski action, the most general class of scalar-tensor theory with at most second-order derivatives in the equations of motion, satisfying theoretical constraints. But these constraints alone are not enough for a given modified gravity model to be physically viable and hence worth studying. In particular, observations place incredibly tight constraints on the size of any deviation in the solar system. Hence, any modified gravity would have to mimic GR in such a situation. To accommodate this requirement, many models invoke screening mechanisms which suppress deviations from GR in regions of high density. But these mechanisms really upon non-linear effects and so studying them in complex models is mathematically complex. To constrain the space of actions of Horndeski type to those which pass solar-system tests, a set of conditions on the four free functions of the Horndeski action are derived which indicate whether a specific model embedded in the action possesses a GR limit. For this purpose, a new and surprisingly simple scaling method is developed, identifying dominant terms in the equations of motion by considering formal limits of the couplings that enter through the new terms in the modified gravity action. Solutions to the dominant terms identify regimes where nonlinear terms dominate and Einstein's field equations are recovered to leading order. Together with an efficient approximation of the scalar field profile, one can determine whether the recovery of Einstein's field equations can be attributed to a genuine screening effect. The parameterised post-Newtonian (PPN) formalism has enabled stringent tests of static weak-field gravity in a theory-independent manner. This is through parameterising common perturbations of the metric found when performing a post-Newtonian expansion. The framework is adapted by introducing an effective gravitational coupling and defining the PPN parameters as functions of position. Screening mechanisms of modified gravity theories can then be incorporated into the PPN framework through further developing the scaling method into a perturbative series. The PPN functions are found through a combination of the scaling method with a post-Newtonian expansion within a screened region. For illustration, we show that both a chameleon and cubic galileon model have a limit where they recover GR. Moreover, we find the effective gravitational constant and all PPN functions for these two theories in the screened limit. To examine how the adapted formalism compares to solar-system tests, we also analyse the Shapiro time delay effect for these two models and find no deviations from GR insofar as the signal path and the perturbing mass reside in a screened region of space. As such, tests based upon the path light rays such as those done by the Cassini mission do not constrain these theories. Finally, gravitational waves have opened up a new regime where gravity can be tested. To this end, we examine how the generation of gravitational waves are affected by theories of gravity with screening to second post-Newtonian (PN) order beyond the quadrupole. This is done for a model of gravity where the black hole binary lies in a screened region, while the space between the binary's neighbourhood and the detector is described by Brans-Dicke theory. We find deviations at both 1.5 and 2 PN order. Deviations of this size can be measured by the Advanced LIGO gravitational wave detector highlighting that our calculation may allow for constraints to be placed on these theories. We model idealised data from the black hole merger signal GW150914 and perform a best fit analysis. The most likely value for the un-screened Brans-Dicke parameter is found to be ω = -1:42, implying on large scales gravity is very modified, incompatible with cosmological results.

Différents environnements gravitationnels à 4 dimensions sont abordés dans ce thése : instantons gravitationnels et trous noirs aussi bien en relativité générale qu'en supergravité. La recherche de nouvelles solutions en relativité est un véritable défi. Cette tâche est nettement simplifiée dans l'hypothèse où l'on dispose d'un tenseur de Riemann auto-dual. Ces solutions sont dites instantons gravitationnels. L'évolution des instantons est décrite par un flot géométrique. Ce lien est analysé en détail, en focalisant l'attention sur le rôle du tensor de Ricci dans le flot géométrique. En espace de type Anti-de-Sitter (AdS), trouver de nouveaux trous noirs avec symétrie axiale est une question toujours ouverte. Cette question peut être posée dans le contexte des fluides holographiques. Trous noirs en rotation correspondent à des fluides aux vorticités particulières. En imposant que la solution soit régulière sur l'horizon, le fluide acquiert la forme d'un fluide parfait. Des conditions nécessaires afin que la correspondence entre solution gravitationnelle et théorie hydrodynamique, qui se fait usuellement par un développement perturbatif, puisse être ressommé et pour qu'on puisse trouver des solutions exactes de la relativité ont etées trouvées. Le comptage de l'entropie des trous noirs dans des espaces AdS ne fait toujours pas partie des résultats connus. Dans le cas des solutions en rotation des théories de supergravité N=2, une relation entre trous noirs extremaux non-BPS en espace plat et trous noirs BPS en espace AdS a été mise au point. La connexion entre cettes solutions donne des informations sur le comptage microscopique.

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

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

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

Différents environnements gravitationnels à 4 dimensions sont abordés dans ce thése : instantons gravitationnels et trous noirs aussi bien en relativité générale qu'en supergravité. La recherche de nouvelles solutions en relativité est un véritable défi. Cette tâche est nettement simplifiée dans l'hypothèse où l'on dispose d'un tenseur de Riemann auto-dual. Ces solutions sont dites instantons gravitationnels. L'évolution des instantons est décrite par un flot géométrique. Ce lien est analysé en détail, en focalisant l'attention sur le rôle du tensor de Ricci dans le flot géométrique. En espace de type Anti-de-Sitter (AdS), trouver de nouveaux trous noirs avec symétrie axiale est une question toujours ouverte. Cette question peut être posée dans le contexte des fluides holographiques. Trous noirs en rotation correspondent à des fluides aux vorticités particulières. En imposant que la solution soit régulière sur l'horizon, le fluide acquiert la forme d'un fluide parfait. Des conditions nécessaires afin que la correspondence entre solution gravitationnelle et théorie hydrodynamique, qui se fait usuellement par un développement perturbatif, puisse être ressommé et pour qu'on puisse trouver des solutions exactes de la relativité ont etées trouvées. Le comptage de l'entropie des trous noirs dans des espaces AdS ne fait toujours pas partie des résultats connus. Dans le cas des solutions en rotation des théories de supergravité N=2, une relation entre trous noirs extremaux non-BPS en espace plat et trous noirs BPS en espace AdS a été mise au point. La connexion entre cettes solutions donne des informations sur le comptage microscopique
The thesis is focused on the study of various gravitational environments in 4 dimensions: gravitational instantons and black holes both in general relativity and in supergravity. In general relativity, the search of new exact solutions is a challenging task. A peculiar simplifying assumption is the one of self-duality of the Riemann tensor. This condition provides a class of gravitational instantons. The temporal evolution of the instantons is described by a geometric flow. This connection has been analyzed in full details. In particular, the role of the Ricci tensor within the geometric flow bas been unraveled. It is a challenging question to exhibit new stationary axysymmetric black holes in AdS space. This question arises in the framework of holographic fluid dynamics. Rotating systems in the bulk correspond to fluids with non-trivial vorticity in the boundary. Regularity of the solution at the horizon implies that the boundary fluid has the form of a perfect-fluid. The holographic correspondence is usually done through a perturbative expansion. Necessary conditions have been found such that the expansion can be resummed and exact solutions of relativity can be generated. A microscopic counting of the entropy of black holes in AdS is not available yet. In the case of N=2 supergravity in four dimensions, a relation between rotating non-BPS extremal asymptotically flat black holes and BPS rotating asymptotically AdS black holes has been discovered. This procedure indicates that, for extremal black holes, a supersymmetric conformal field theory dual can be found, thus gaining insights on the role of gaugings in the microscopic counting

A presente dissertação tem como objeto de estudo sistemas da física da matéria condensada que sejam capazes de simular sistemas gravitacionais, tais como buracos negros e universos em expansão, onde processos quânticos tomam parte. Neste estudo nos debruçamos principalmente sobre o modelo do fluido e condensados de Bose-Einstein. No modelo do fluido exploramos a geometria efetiva que surge e os problemas de back-reaction e dos modos trans-planckianos de campos quânticos. No modelo baseado em condensados exploramos sua faceta cosmológica e a possibilidade de campos maciços. Além destes dois modelos de grande relevância na literatura, ainda expomos os análogos em cordas elásticas e os baseados em ondas na superfícies de fluidos e uma análise geral baseada no formalismo lagrangeano para campos.
This dissertation has as object of study systems of condensate-matter physics which can simulate gravitational systems like black holes and expanding universes where quantum processes take place. In this study we lay attention mainly on the fluid model and on Bose-Einstein-condensate-based models. In the fluid model we explore the features of the emergent geometry and other problems like the back-reaction and the trans-planckian modes of quantum fields. In the condensate-based models we explore their cosmological aspects and the possibility for massive fields. Moreover, we shall present two other models, the elastic string and the surface-wave-based models in fluids, and a very general analysis based on the Lagrangean formalism for fields.

One of the most exciting predictions of Einstein's theory of gravitation that have not yet been proven experimentally by a direct detection are gravitational waves. These are tiny distortions of the spacetime itself, and a world-wide effort to directly measure them for the first time with a network of large-scale laser interferometers is currently ongoing and expected to provide positive results within this decade. One potential source of measurable gravitational waves is the inspiral and merger of two compact objects, such as binary black holes. Successfully finding their signature in the noise-dominated data of the detectors crucially relies on accurate predictions of what we are looking for. In this thesis, we present a detailed study of how the most complete waveform templates can be constructed by combining the results from (A) analytical expansions within the post-Newtonian framework and (B) numerical simulations of the full relativistic dynamics. We analyze various strategies to construct complete hybrid waveforms that consist of a post-Newtonian inspiral part matched to numerical-relativity data. We elaborate on exsisting approaches for nonspinning systems by extending the accessible parameter space and introducing an alternative scheme based in the Fourier domain. Our methods can now be readily applied to multiple spherical-harmonic modes and precessing systems. In addition to that, we analyze in detail the accuracy of hybrid waveforms with the goal to quantify how numerous sources of error in the approximation techniques affect the application of such templates in real gravitational-wave searches. This is of major importance for the future construction of improved models, but also for the correct interpretation of gravitational-wave observations that are made utilizing any complete waveform family. In particular, we comprehensively discuss how long the numerical-relativity contribution to the signal has to be in order to make the resulting hybrids accurate enough, and for currently feasible simulation lengths we assess the physics one can potentially do with template-based searches.
Eine der aufregendsten Vorhersagen aus Einsteins Gravitationstheorie, die bisher noch nicht direkt durch ein Experiment nachgewiesen werden konnten, sind Gravitationswellen. Dies sind winzige Verzerrungen der Raumzeit selbst, und es wird erwartet, dass das aktuelle Netzwerk von groß angelegten Laserinterferometern im kommenden Jahrzehnt die erste direkte Gravitationswellenmessung realisieren kann. Eine potentielle Quelle von messbaren Gravitationswellen ist das Einspiralen und Verschmelzen zweier kompakter Objekte, wie z.B. ein Binärsystem von Schwarzen Löchern. Die erfolgreiche Identifizierung ihrer charakteristischen Signatur im Rausch-dominierten Datenstrom der Detektoren hängt allerdings entscheidend von genauen Vorhersagen ab, was wir eigentlich suchen. In dieser Arbeit wird detailliert untersucht, wie die komplettesten Wellenformenmodelle konstruiert werden können, indem die Ergebnisse von (A) analytischen Entwicklungen im post-Newtonschen Verfahren und (B) numerische Simulationen der voll-relativistischen Bewegungen verknüpft werden. Es werden verschiedene Verfahren zur Erstellung solcher "hybriden Wellenformen", bei denen der post-Newtonsche Teil mit numerischen Daten vervollständigt wird, analysiert. Existierende Strategien für nicht-rotierende Systeme werden vertieft und der beschriebene Parameterraum erweitert. Des Weiteren wird eine Alternative im Fourierraum eingeführt. Die entwickelten Methoden können nun auf multiple sphärisch-harmonische Moden und präzedierende Systeme angewandt werden. Zusätzlich wird die Genauigkeit der hybriden Wellenformen mit dem Ziel analysiert, den Einfluss verschiedener Fehlerquellen in den Näherungstechniken zu quantifizieren und die resultierenden Einschränkungen bei realen Anwendungen abzuschätzen. Dies ist von größter Bedeutung für die zukünftige Entwicklung von verbesserten Modellen, aber auch für die korrekte Interpretation von Gravitationswellenbeobachtungen, die auf Grundlage solcher Familien von Wellenformen gemacht worden sind. Insbesondere wird diskutiert, wie lang der numerische Anteil des Signals sein muss, um die Hybride genau genug konstruieren zu können. Für die aktuell umsetzbaren Simulationslängen wird die Physik eingeschätzt, die mit Hilfe von Modell-basierten Suchen potentiell untersucht werden kann.

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

The correspondence of stationary, axisymmetric, asymptotically flat space-times and bundles over a reduced twistor space has been established in four dimensions. The main impediment for an application of this correspondence to examples in higher dimensions is the lack of a higher-dimensional equivalent of the Ernst poten- tial. This thesis will propose such a generalized Ernst potential, point out where the rod structure of the space-time can be found in the twistor picture and thereby provide a procedure for generating solutions to the Einstein field equations in higher dimensions from the rod structure, other asymptotic data, and the requirement of a regular axis. Examples in five dimensions are studied and necessary tools are developed, in particular rules for the transition between different adaptations of the patching matrix and rules for the elimination of conical singularities.

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

The expectation that light waves are the only way to gather information about the distant universe dominated scientific thought, without serious alternative, until Einstein’s 1916 proposal that gravitational waves are generated by the dynamics of massive objects. Now, after nearly a century of speculation, theoretical development, observational support, and finally, tremendous experimental preparation, there are good reasons to believe that we will soon directly detect gravitational waves. One of the most important of these good reasons is the fact that matched filtering enables us to dig gravitational wave signals out of noisy data, if we have prior information about the signal’s morphology. Thus, at the interface of Numerical Relativity simulation, and data analysis for experiment, there is a central effort to model likely gravitational wave signals. In this context, I present my contributions to the modeling of Gravitational Ringdown (Kerr Quasinormal Modes). Specifically by ap- propriately interfacing black hole perturbation theory with Numerical Relativity, I present the first robust models for Quasinormal Mode excitation. I present the first systematic de- scription of Quasinormal Mode overtones in simulated binary black hole mergers. I present the first systematic description of nonlinear Quasinormal Mode excitation in simulated bi- nary black hole mergers. Lastly, it is suggested that by analyzing the phase of black hole Quasinormal Modes, we may learn information about the black hole’s motion with respect to the line of sight. Moreover, I present ongoing work at the intersection of gravitational wave modeling and machine learning. This work shows promise for the automated and near optimal placement of Numerical Relativity simulations concurrent with the near optimal linear modeling of gravitational output.

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

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.

Gravitation is the dominant influence in most astrophysical interactions. Weak-field interactions have been extensively studied, but the strong-field regime remains largely unexplored. Gravitational waves (GWs) are an excellent means of accessing strong-field regions. We investigate what we can learn about both astrophysics and gravitation from strong-field tests and, in particular, GWs; we focus upon extreme-mass-ratio (EMR) systems where a small body orbits a much more massive one. EMR bursts, a particular class of GW signals, could be used to determine the properties of massive black holes (MBHs). They could be detectable with a space-borne interferometer from many nearby galaxies, as well as the Galactic centre. Bursts could provide insightful constraints on the MBHs' parameters. These could elucidate the formation history of the MBHs and, by association, their host galaxies. The Galactic centre is the most promising source. Its event rate is determined by the stellar distribution surrounding the MBH; the rate is not high, but we still expect to gain useful astronomical information from bursts. Strong-field tests may reveal deviations from general relativity (GR). We calculate modifications that could be observed assuming metric f(R)-gravity as an effective alternative theory. Gravitational radiation is modified, as are planetary precession rates. Both give a means of testing GR. However, existing laboratory measurements already place tighter constraints on f(R)-gravity, unless there exists a screening effect, such as the chameleon mechanism, which suppresses modifications on small scales. To make precision measurements of astrophysical systems or place exacting bounds on deviations from GR, we must have accurate GW templates. Transient resonances are currently not included in the prescription for generating EMR inspiral waveforms. Their effects can be estimated from asymptotic expansions of the evolving orbital parameters. The quantitative impact on parameter estimation has yet to be calculated, but it appears that it shall be necessary to incorporate resonances when creating inspiral waveforms.

The fuzzball model of a black hole is an attempt to resolve the many paradoxes and puzzles of black hole physics that have revealed themselves over the last century. These badly behaved solutions of general relativity have given physicists one of the few laboratories to test candidate quantum theories of gravity. Though little is known about exactly what lies beyond the event horizon, and what the ultimate fate of matter that falls in to a black hole is, we know a few intriguing and elegant semi-classical results that have kept physicists occupied. Among these are the known black hole entropy and the Hawking radiation process.

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

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 fuzzball model of a black hole is an attempt to resolve the many paradoxes and puzzles of black hole physics that have revealed themselves over the last century. These badly behaved solutions of general relativity have given physicists one of the few laboratories to test candidate quantum theories of gravity. Though little is known about exactly what lies beyond the event horizon, and what the ultimate fate of matter that falls in to a black hole is, we know a few intriguing and elegant semi-classical results that have kept physicists occupied. Among these are the known black hole entropy and the Hawking radiation process.

Depuis sa formulation au début du 20ème siècle, la théorie de la Relativité Générale a été vérifiée avec une précision sans cesse croissante. Cette théorie prédit, entre autre, l'existence d'ondes gravitationnelles qui restent à ce jour inobservées, et ce malgré de nombreuses tentatives de détections. Ces ondes sont caractérisées par leur absence de masse. Une des questions qui se pose alors est de savoir si cette absence de masse est une condition nécessaire pour que théorie et observations concordent. Pour répondre à cette question, il est indispensable d'étudier les différents aspects des théories décrivant des ondes gravitationnelles massives. Au-delà de cet intérêt purement théorique, l'étude de ces théories est, entre autre, motivée par de récentes observations cosmologiques. Celles-ci indiquent que l'accord entre la Relativité Générale et les observations n'est possible que si on suppose l'existence de matière et d'énergie noires.

Cette thèse est dédiée à une classe de théories décrivant des ondes gravitationnelles massives. Dans un premier temps, nous résumons les différents problèmes qui surgissent lorsqu'on tente de donner une masse aux ondes gravitationnelles. Ensuite, nous introduisons une classe de modèles et étudions certaines de leurs caractéristiques.

Le premier aspect étudié concerne l'existence d'une interaction de type instantanée. De telles interactions sont possibles étant donné que l'invariance de Lorentz est spontanément brisée dans les modèles considérés. Celles-ci sont dès lors discutées et un exemple concret est fourni.

La présence d'une interaction instantanée dans ces modèles a une conséquence directe sur les solutions "trous noirs" des équations du champ. En effet, on s'attend à ce que l'interaction instantanée puisse propager de l'information à l'extérieur d'un trou noir, ce qui entraînerait une modification de ces solutions par rapport à celles de la Relativité Générale. Cette supposition est confirmée par les solutions "trous noirs" obtenues dans cette thèse. Celles-ci peuvent soit imiter une certaine quantité de matière noire, soit conduire à un champ gravitationnel répulsif.

Finalement, les mécanismes de formation des grandes structures de l'Univers (galaxies, amas de galaxies, ) sont étudiés pour les théories considérées. Cette dernière discussion démontre que ces modèles reproduisent le comportement prévu par la Relativité Générale et sont, par conséquent, en accord avec les observations.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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

Nous étudions les champs de Maxwell à l'extérieur de trous noirs de Reissner-Nordstrom-de Sitter. Nous commençons par étudier la géométrie de ces espaces-temps : nous donnons une condition sous laquelle la métrique admet trois horizons puis dans ce cadre nous construisons l'extension analytique maximale d'un trou noir de Reissner-Nordstrom-de Sitter. Nous donnons ensuite une description générale des champs de Maxwell en espace-temps courbe, de leur décomposition en composantes spinorielle ainsi que de leur énergie. La première étude analytique établit la décroissance ponctuelle de champs de Maxwell à l'extérieur d'un trou noir de Reissner-Nordstrom-de Sitter ainsi que la décroissance uniforme de l'énergie sur un hyperboloïde qui s'éloigne dans le futur. Ce chapitre utilise des méthodes de champs de vecteurs (estimations d'énergie géométriques) dans l'esprit des travaux de Pieter Blue. Enfin nous construisons une théorie du scattering conforme pour les champs de Maxwell à l'extérieur du trou noir. Ceci consiste en la résolution du problème de Goursat pour les champs de Maxwell à la frontière isotrope de l'extérieur du trou noir, constituée des horizons du trou noir et horizons cosmologiques futurs et passés. Les estimations de décroissance uniforme de l'énergie sont cruciales dans cette partie
We study Maxwell fields on the exterior of Reissner-Nordstrom-de Sitter black holes. We start by studying the geometry of these spacetimes: we give the condition under which the metric admits three horizons and in this case we construct the maximal analytic extension of the Reissner-Nordstrom-de Sitter black hole. We then give a general description of Maxwell fields on curves spacetimes, their decomposition into spin components, and their energies. The first result establishes the pointwise decay of the Maxwell field in the exterior of a Reissner-Nordstrom-de Sitter black hole, as well as the uniform decay of the energy flux across a hyperboloid that recedes in the future. This chapter uses the vector fields methods (geometric energy estimates) in the spirit of the work of Pieter Blue. Finally, we construct a conformal scattering theory for Maxwell fields in the exterior of the black hole. This amounts to solving the Goursat problem for Maxwell fields on the null boundary of the exterior region, consisting of the future and past black hole and cosmological horizons. The uniform decay estimates of the energy are crucial to the construction of the conformal scattering theory

In this thesis I present three separate studies on three different topics in General Relativity. The first study investigates the accuracy with which the mass and angular momentum of a black hole can be determined by measurements of gravitational waves from the hole, using a laser-interferometer gravitational-wave detector. The black hole is assumed to have been strongly perturbed, perhaps by coalescence with a binary companion, and the detector measures the waves produced by its resulting vibration and ring-down. The uncertainties in the measured mass and angular momentum arise from the unavoidable presence of noise in the detector. It is found that the faster the hole rotates, the more accurate the measurements will be, with the uncertainty in the angular momentum decreasing rapidly with increasing rotation speed. It is also found that the errors in the mass and angular momentum are highly correlated. The second study is an analysis of the gravitational collapse of an infinitely long, cylindrical dust shell. This analysis is expected to be helpful in understanding the behavior during collapse of more realistic, finite-length bodies. It is found that the collapse evolves into a naked singularity in finite time, as measured by a distant observer or by one riding on the shell. Analytical expressions for the variables describing the collapse are found at late times, near the singularity. The picture is completed with a numerical simulation that follows the collapse from the start until very close to the singularity. The singularity is found to be strong, in the sense that an observer riding on the shell will be infinitely stretched in the direction parallel to the symmetry axis, and infinitely compressed in the azimuthal direction. The gravitational waves emitted from the collapse are also analyzed. The last study focuses on a different kind of phenomenon, namely, the consequences of the existence of closed timelike curves in a spacetime that contains a wormhole. One might expect that the closed timelike curves would cause difficulty for the initial value problem for systems that evolve in such a spacetime: a system with apparently well-posed initial conditions might have no self-consistent solutions to its evolution equations. We study the simple case of a macroscopic, classical particle with a hard-sphere potential (a "billiard ball"), and we focus attention on initial conditions for which the evolution, if followed naively, is self- inconsistent: the ball enters one mouth of the wormhole and then comes out of the other mouth at an earlier time, then collides with its younger self, preventing itself from ever entering the first mouth. We find, surprisingly, that for all such "dangerous" initial conditions, there are an infinite number of self-consistent evolutionary solutions, involving a glancing collision and any number of wormhole traversals. We also find that for many non-dangerous initial conditions, there also exist an infinity of possible evolutions.

L'existence de la masse négative a un sens parfaitement physique du moment que les conditions d'énergie dominante sont satisfaites par le tenseur énergie-impulsion correspondant. Jusqu'à maintenant, seules des configurations de masses négatives avaient été trouvées. On démontre l'existence de bulles de masse négative stables dans un espace-temps qui s'approche asymptotiquement d'un espace-temps de de Sitter. Les bulles sont des solutions aux équations d'Einstein qui correspondent à une région intérieure qui contient une distribution de masse spécifique séparée par une coquille mince de l'espace-temps à masse négative de Schwarzschild-de Sitter à l'extérieur. Ensuite, on applique les conditions de jonction d'Israel à la frontière de la bulle ce qui impose la conservation d'énergie-impulsion à travers la surface. Les conditions de jonction donnent une équation pour un potentiel pour le rayon de la bulle qui dépend de la distribution de masse à l'intérieur, ou vice versa. Finalement, on trouve un potentiel qui aboutit à une solution stable, statique et non-singulière, ce qui crée une distribution de masse interne qui satisfait les conditions d'énergie dominante partout à l'intérieur. Cependant, la bulle ne satisfait pas ces conditions. De plus, on trouve une solution stable, statique et non-singulière pour une géométrie interne de de Sitter pure. La solution est fondamentalement différente: elle requiert que la densité d'énergie de la bulle change avec le rayon. La condition d'énergie dominante est satisfaite partout.
Negative mass makes perfect physical sense as long as the dominant energy condition is satisfied by the corresponding energy-momentum tensor. Until now, only configurations of negative mass have been found. We demonstrate the existence of stable, negative-mass bubbles in an asymptotic de Sitter space-time. The bubbles are solutions of the Einstein equations which correspond to an interior region of space-time containing a specific distribution of mass separated by a thin wall from the exact, negative mass Schwarzschild-de Sitter space-time in the exterior. Then, we apply the Israel junction conditions at the wall which impose the conservation of energy and momentum across the wall. The junction conditions give rise to an effective potential for the radius of the wall that depends on the interior mass distribution, or vice versa. Finally, we find a potential that gives rise to stable, non-singular, static solutions, which yields an interior mass distribution that everywhere satisfies the dominant energy condition. However, the energy momentum of the wall does not satisfy the dominant energy condition. Moreover, we find a stable, non-singular, static solution for a pure de Sitter geometry inside the bubble. The solution is fundamentally different: the energy density of the bubble is no longer a constant, but now varies with the radius. The dominant energy condition is everywhere satisfied.

Dumb holes (also known as acoustic black holes) are fluid flows which include an "acoustic horizon:" a surface, analogous to a gravitational horizon, beyond which sound may pass but never classically return. Soundwaves in these flows will therefore experience "effective geometries" which are identical to black hole spacetimes up to a conformal factor. By adjusting the parameters of the fluid flow, it is possible to create an effective geometry which is conformal to the Anti-de Sitter black hole spacetime- a geometry which has recieved a great deal of attention in recent years due to its conjectured holographic duality to Conformal Field Theories. While we would not expect an acoustic analogue of the AdS-CFT correspondence to exist, this dumb hole provides a means, at least in principle, of experimentally testing the theoretical properties of the AdS spacetime. In particular, I have calculated the quasinormal mode spectrum of this acoustic geometry.
Graduate
0986
0753
jpbabb@yahoo.ca