In this thesis we discuss drawbacks of the event horizon which is defined glo- bally in spacetime and we introduce a quasilocal definition of black hole boundary foliated by marginally trapped surfaces on which the expansion of the outer null normal congruence becomes zero. List of different types of quasilocal horizons follows, i.e. apparent horizon, trapping horizon and isolated and dynamical hori- zon. Subsequently we calculate and analyse quasilocal horizons in two dynamical spacetimes which are used as inhomogeneous cosmological models. We discover future and past horizon in spherically symmetric Lemaître spacetime and we come to conclusion that both are null and have locally the same geometry as the ho- rizons in the LTB spacetime. Then we study Szekeres-Szafron spacetime with no symmetries, particularly its subfamily with β,z ̸= 0, and we derive the equation of the horizon. However, because of the lack of symmetries the spacetime is not adapted to double-null foliation, therefore we were unsuccessful in our attempts to estimate the equation's solution. Only in a special case when the function Φ does not depend on the coordinate z we found a condition on the existence of the horizon, that is Φ,t Φ > 0. 1

While the formalism of isolated horizons is known for some time, only quite recently the near horizon solution of Einstein's equations has been found in the Bondi-like coordinates by Krishnan in 2012. In this framework, the space-time is regarded as the characteristic initial value problem with the initial data given on the horizon and another null hypersurface. It is not clear, however, what ini- tial data reproduce the simplest physically relevant black hole solution, namely that of Kerr-Newman which describes stationary, axisymmetric black hole with charge. Moreover, Krishnan's construction employs the non-twisting null geodesic congruence and the tetrad which is parallelly propagated along this congruence. While the existence of such tetrad can be easily established in general, its explicit form can be very difficult to find and, in fact it has not been provided for the Kerr-Newman metric. The goal of this thesis was to fill this gap and provide a full description of the Kerr-Newman metric in the framework of isolated horizons. In the theoretical part of the thesis we review the spinor and Newman-Penrose formalism, basic geometry of isolated horizons and then present our results. Thesis is complemented by several appendices.

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.

Classical theory cannot provide a satisfying scenario for a unitary thermodynamic evolution of black holes. To preserve information one requires quantum mechanical effects on scales reaching beyond the traditional horizon radius. Therefore, common to many of the theories attempting to resolve the paradox is the existence of exotic horizon structures. The recent advent of gravitational wave astronomy provides a possible means for detecting the existence of such structures through gravitational wave emission in the ringdown phase of binary black hole mergers. Such emission is described by quasinormal modes (QNMs) in which the gravitational waves originates outside the black hole, in the vicinity of the photon spheres. Requiring reflective properties of the horizon structure results in the existence of gravitational echoes that may be detected by facilities such as LIGO etc.. This thesis studies geodesic motion of such echoes in the equatorial plane of a rotating black hole. Depending on the extent of the horizon structure, and the particular mode of emission, one can expect different timescales for the echoes. For a horizon structure extending <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5CLambda%20r%20=" /> <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?10%5E%7B-12%7D" /> <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?M" /> outside the traditional horizon of a  <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?M%20=%2022.6%20M_%7B%5Codot%7D" />, <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?a%20=%200.74%20M" /> black hole one would ideally find echoes appearing as integer multiples of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5CDelta%20t_%7Becho%7D" /><img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?=%200.0204%20s" /> after the primary signal. The time delay is expected to increase by at least an order of magnitude if one lets <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5CDelta%20r%20%5Csim%2010%5E%7B-80%7D%20M" />. The expected echo timescales for gravitational waves emitted from any point around the black hole, in arbitrary modes, is an interesting further study.

The black hole information paradox arises when quantum mechanical effects are considered in the vicinity of the event horizon of a black hole. In this report we describe the fundamental properties of quantum mechanical systems and black holes that lead to the information paradox, with focus on quantum entanglement. While first presented in 1976, the information paradox is as of yet an unsolved problem. Two of the proposed solutions, black hole complementarity and firewalls, are discussed. / Svarta hålets informationsparadox uppkommer när man tar hänsyn till kvantmekaniska effekter i närheten av händelsehorisonten av ett svart hål. I denna rapport beskrivs de grundläggande egenskaper hos kvantmekaniska system och svarta hål som leder till informationsparadoxen, med fokus på kvantintrassling. Paradoxen, som presenterades 1976 men än idag är ett olöst problem, förklaras sedan. Två av de förslagna lösningarna till paradoxen, svarta hål-komplementaritet och firewalls, diskuteras.

La solution des équations d'Einstein–Maxwell décrivant le trou noir le plus général a été découverte par Plebański et Demiański en 1976. Cette thèse accomplit plusieurs étapes en vue d'intégrer une généralisation de cette solution en supergravité jaugée N = 2. Le contenu bosonique de cette dernière comprend la métrique assortie de champs de jauge et de deux types de champs scalaires (appelés scalaires-vecteurs et hyperscalaires); cela implique qu'il est beaucoup plus compliqué de trouver une solution générale et l'on doit se restreindre à des classes particulières de solutions ou bien utiliser des algorithmes pour générer des solutions.Dans la première partie de cette thèse nous approchons ce problème grâce à la première stratégie en nous restreignant aux solutions BPS.Dans un premier temps nous étudions les jaugeages abéliens qui impliquent les hyperscalaires afin de comprendre quelles sont les conditions nécessaires pour obtenir des vides N = 2 adS4 ainsi que des géométries de proche-horizon associées à des trous noirs statiques.Par la suite nous décrivons une solution générale et analytique pour des trous noirs (extrémaux) 1/4-BPS qui possèdent une masse, une charge de NUT, des charges dyoniques et des champs scalaires non-triviaux dans le contexte de la supergravité N = 2 jaugée à la Fayet–Iliopoulos.Dans la seconde partie nous obtenons une extension de l'algorithme de Janis-Newman afin de prendre en compte tous les champs bosoniques de spin inférieur à 2, les horizons topologiques et le cas des autres dimensions.Ainsi cela met à disposition tous les outils nécessaires pour appliquer cet algorithme à la supergravité (jaugée ou non). / The most general black hole solution of Einstein–Maxwell theory has been discovered by Plebański and Demiański in 1976.This thesis provides several steps towards generalizing this solution by embedding it into N = 2 gauged supergravity.The (bosonic fields of the) latter consists in the metric together with gauge fields and two kinds of scalar fields (vector scalars and hyperscalars); as a consequence finding a general solution is involved and one needs to focus on specific subclasses of solutions or to rely on solution generating algorithms. In the first part of the thesis we approach the problem using the first strategy: we restrict our attention to BPS solutions, relying on a symplectic covariant formalism. First we study the possible Abelian gaugings involving the hyperscalars in order to understand which are the necessary conditions for obtaining N = 2 adS4 vacua and near-horizon geometries associated to the asymptotics of static black holes.A preliminary step is to obtain covariant expressions for the Killing vectors of symmetric special quaternionic-Kähler manifolds. Then we describe a general analytic solutions for 1/4-BPS (extremal) black holes with mass, NUT, dyonic charges and running scalars in N = 2 Fayet–Iliopoulos gauged supergravity with a symmetric very special Kähler manifold. In the second part we provide an extension of the Janis–Newman algorithm to all bosonic fields with spin less than 2, to topological horizons and to other dimensions. This provides all the necessary tools for applying this solution generating algorithm to (un)gauged supergravity, and interesting connections with the N = 2 supergravity theory are unravelled.

In this thesis, the stability of the family of subextremal Kerr-Newman space- times is studied in the case of linear scalar perturbations. That is, nondegenerate energy bounds (NEB) and integrated local energy decay (ILED) results are proved for solutions of the wave equation on the domain of outer communications. The main obstacles to the proof of these results are superradiance, trapping and their interaction. These difficulties are surmounted by localising solutions of the wave equation in phase space and applying the vector field method. Miraculously, as in the Kerr case, superradiance and trapping occur in disjoint regions of phase space and can be dealt with individually. Trapping is a high frequency obstruction to the proof whereas superradiance occurs at both high and low frequencies. The construction of energy currents for superradiant frequencies gives rise to an unfavourable boundary term. In the high frequency regime, this boundary term is controlled by exploiting the presence of a large parameter. For low superradiant frequencies, no such parameter is available. This difficulty is overcome by proving quantitative versions of mode stability type results. The mode stability result on the real axis is then applied to prove integrated local energy decay for solutions of the wave equation restricted to a bounded frequency regime. The (ILED) statement is necessarily degenerate due to the trapping effect. This implies that a nondegenerate (ILED) statement must lose differentiability. If one uses an (ILED) result that loses differentiability to prove (NEB), this loss is passed onto the (NEB) statement as well. Here, the geometry of the subextremal Kerr-Newman background is exploited to obtain the (NEB) statement directly from the degenerate (ILED) with no loss of differentiability.

Orientadores: Alberto Vazquez Saa, Marcus Aloizio Martinez de Aguiar / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-27T13:28:54Z (GMT). No. of bitstreams: 1 Vieira_RonaldoSavioliSume_D.pdf: 9121576 bytes, checksum: eab8bcedfd86d048afd51f4b65fe9501 (MD5) Previous issue date: 2015 / Resumo: Neste trabalho analisamos aspectos dinâmicos de sistemas astrofísicos que possuem uma componente discoidal proeminente. Estudamos o movimento de partículas de teste (estrelas) que cruzam discos galácticos bidimensionais e axialmente simétricos, obtendo uma fórmula para o envelope das órbitas que depende somente da densidade superficial $\Sigma$ do disco. Essa fórmula nos dá uma terceira integral de movimento aproximada para o sistema. Também analisamos a estabilidade das órbitas circulares equatoriais nesses discos, chegando à condição de estabilidade vertical $\Sigma>0$. Esse formalismo é estendido para discos tridimensionais, assim como para a relatividade geral (em que obtivemos que a \textit{condição de energia forte} é suficiente para a estabilidade vertical das órbitas circulares em discos infinitesimais, no caso estático e axialmente simétrico). Trabalhamos também com a aproximação pós-newtoniana (1PN), obtendo o formalismo hamiltoniano para uma distribuição arbitrária de matéria, assim como as correções 1PN nas frequências epicíclicas radial e vertical para configurações estacionárias e axialmente simétricas e a terceira integral de movimento aproximada para discos infinitesimais (estacionários). Outro resultado obtido foi a dependência das frequências epicíclicas com a curvatura riemanniana do espaço-tempo para distribuições suaves de matéria-energia, no caso estático e axialmente simétrico em relatividade geral. A segunda parte desta tese corresponde aos resultados para discos de acreção. Analisamos o movimento de partículas de teste na métrica de Kehagias & Sfetsos (solução esfericamente simétrica da gravitação de Horava no caso em que o espaço-tempo é assintoticamente plano), na região de parâmetros em que a singularidade central é nua. Por fim, estudamos a espessura dos discos de acreção super-Eddington obtida por simulações globais recentes de radiation magnetohydrodynamics em relatividade geral. O resultado foi comparado com modelos de discos slim para taxas de acreção similares, levando à conclusão de que o estado final (estacionário) dos fluxos de acreção gerados por essas simulações é um disco slim, e não um disco espesso, como seria esperado pelas características das configurações iniciais do tipo Polish Doughnuts usualmente adotadas / Abstract: In this work, we analyze dynamical aspects of astrophysical systems containing a prominent discoidal component. We study the motion of test particles (stars) which cross bidimensional, axially symmetric galactic disks, obtaining a formula for the orbits' envelope which depends solely on the disk's surface density. This formula gives us an approximate third integral of motion for the system. We also analyze the stability of equatorial circular orbits in these disks, arriving at the vertical stability condition $\Sigma>0$. This formalism is extended to three-dimensional disks, as well as to general relativity (in which we obtained that the \textit{strong energy condition} is sufficient for vertical stability of circular orbits in infinitesimal disks, in the static and axially symmetric case). We also worked with the post-Newtonian approximation (1PN), obtaining the Hamiltonian formalism for an arbitrary matter distribution, as well as the 1PN corrections to the radial and vertical epicyclic frequencies for stationary and axially symmetric configurations, and the approximated third integral of motion for (stationary) infinitesimal disks. Another result obtained was the dependence of the epicyclic frequencies on the Riemannian spacetime curvature for smooth matter-energy distributions, in the static and axially symmetric case. The second part of this thesis corresponds to the results concerning accretion disks. We analyzed the motion of test particles in the Kehagias & Sfetsos metric (spherically symmetric solution to Horava's gravity in the case in which the spacetime is asymptotically flat), in the parameter region in which the singularity is naked. Finally, we studied the thickness of super-Eddington accretion disks, obtained via recent global radiation magnetohydrodynamics simulations in general relativity. The result was compared with slim-disk models for similar accretion rates, leading to the conclusion that the final (stationary) state of accretion flows generated by these simulations is a slim disk, and not a thick disk, as it would be expected by the characteristics of the usually adopted Polish Doughnuts initial configurations / Doutorado / Física / Doutor em Ciências

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Cette thèse est consacrée à la dynamique globale d’un fluide évoluant dans le domaine de communication extérieur d’un espace-temps de Schwarzschild. Dans le premier chapitre, on formule le problème de Cauchy pour le modèle d’Euler relativiste dans la classe des solutions à la variation bornée contenant des ondes de choc. On propose ensuite une version de la méthode de Glimm fondée sur les solutions stationnaires globales hors du trou noir et le problème de Riemann généralisé et on démontre un théorème d’existence globale en temps pour les écoulements de fluides faiblement réguliers. Dans le deuxième chapitre, on considère le modèle de Burgers relativiste. Nous introduisons une version de la variation totale qui est décroissante en temps pour les solutions générales du problème de Cauchy. Nous avons aussi utilisé les caractéristiques généralisées pour démontrer la stabilité nonlinéaire d’une solution stationnaire par morceaux. Dans le troisième chapitre, nous pr étudions plusieurs méthodes numériques basées sur la géométrie de Schwarzschild et nous étudions numériquement la stabilité nonlinéaire des solutions stationnaires et le comportement asymptotique des solutions générales. Les schémas propos ́es fournissent un outils numérique capable de préserver exactement les équilibres et nous permettent d’analyser l’evolution de fluides en présence d’effets géométriques. Dans le quatrième chapitre, nous présentons un modèle non-relativiste préservant certains effets du trou noir de Schwarzschild. / This thesis is devoted to fluid dynamics evolving in the domain of outer communication of a Schwarzschild black hole. In the first chapter, we formulate the initial value problem of the relativistic Euler model within a class of weak solutions with bounded variation, possibly containing shock waves. We then introduce a version of the random choice method founded on the global steady state solutions and the generalized Riemann problem and we establish a global-in-time existence theory for the initial value problem within the proposed class of weakly regular fluid flows. In the second chapter, we consider the relativistic Burgers model. We have introduced a version of the total variation which is decreasing with respect to time in the Cauchy problem. We also use the generalized characteristics to prove the nonlinear stability of a piecewise steady state solution. In the third chapter, we present some numerical methods based on the Schwarzschild geometry and study numerically the nonlinear stability of steady state solutions and the asymptotic behavior of a general solutions. The proposed schemes provide a numerical tool capable to preserve exactly the equilibria and allow us to analyse the evolution of fluids with the geometry effects.