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Supermassive black holes (SMBH) are now thought to exist at the center nearly all massive galaxies. Not only are they thought to be ubiquitous, but it was also discovered nearly two decades ago that the mass of these SMBHs correlate strongly with properties of their host galaxies including bulge stellar velocity dispersion (MBH-sigma) and bulge luminosity (MBH-Lbulge). This correlation was not expected due to the tiny size of the SMBH gravitational sphere of influence compared to the size of the host galaxy, and imply a connection between the two, but this connection is still not well-understood. One step toward understanding this connection is to accurately measure the masses of these black holes. Two of the most common direct SMBH mass measurement techniques are stellar dynamical modeling (SDM), which generally only applies to quiescent galaxies, and reverberation mapping (RM), which can only be applied to active galactic nuclei (AGN) that exhibit broadened emission lines. Due to the unknown geometry of the region that produces these broad lines, the whole RM sample of black hole masses generally needs to be multiplied by a constant called the f-factor to bring it into agreement with the SDM sample on the MBH-sigma relation. It is unknown how well this f-factor, being a population average, applies to individual RM masses. It would therefore be useful to measure an SMBH mass with both methods simultaneously to test whether they produce the same black hole mass. However, because the RM and SDM techniques usually apply to galaxies that are not possible for both, this has only been attempted twice before (NGC 3227 and NGC 4151). The purpose of this dissertation is to apply SDM to the SMBH at the center of NGC 6814 for which there already exists an RM mass. This makes it only the third broad-lined AGN for which an SDM mass has been derived. In order to perform SDM accurately, the distance to the galaxy needs to be well-constrained as the error in the SDM mass scales linearly with distance. Because no adequate distance measurements already exist, the first half of this dissertation is devoted to deriving a Cepheid distance to NGC 6814 from V- and I-band HST WFC3 time series photometry. We measure the distance to NGC 6814 to be 17.54 +1.44/-1.33 Mpc. In the second half, we incorporate that distance measurement into our stellar dynamical modeling on Gemini NIFS+Altair IFU data of NGC 6814's central 1.55''x1.55''. We derive a mass of 1.19 +37.57/-1.17 x108 solar masses, and best fit mass-to-light ratio of 0.948 +0.032/-0.208 in solar units. This mass is nearly an order of magnitude larger than the RM mass but has a 3-sigma range spanning nearly three orders of magnitude. We describe possible reasons for our larger-than-expected mass value, such as the existence of a bar, which would not be well-modeled by an axisymmetric dynamical code. Finally, we describe future steps that may be taken to better constrain the mass, such as creating more models to further explore parameter space.

The motion of a test particle in the Schwarzschild background models the merger of a compact object binary with extremely different masses known in the literature as Extreme Mass Ratio Inspiral. In the simplest geodesic approxima- tion, this motion is integrable and there is no chaos. When one takes the spin of the smaller body into account, integrability is broken and prolonged resonances along with chaotic orbits appear. By employing the methods of Poincaré surface of section, rotation number and recurrence analysis we show for the first time that there is chaos for astrophysically relevant spin values. We propose a uni- versal method of measuring widths of resonances in perturbations of geodesic motion in the Schwarzschild spacetime using action-angle-like variables. We ap- ply this novel method to demonstrate that one of the most prominent resonances is driven by second order in spin terms by studying its growth, supporting the expectation that chaos will not play a dominant role in Extreme Mass Ratio Inspirals. Last but not least, we compute gravitational waveforms in the time- domain and establish that they carry information on the motion's dynamics. In particular, we show that the time series of the gravitational wave strain can be used to discern regular from chaotic motion of the source. 1

L’intérêt majeur des travaux exposés dans cette thèse est d’explorer la chevelure des trous noirs dans des cadres plus généraux que celui de la Relativité Générale en tenant compte de la présence d’une constante cosmologique, de dimensions supplémentaires, de champs de matière exotiques ou de termes de courbure de rang plus élevé. Ces extensions de la Relativité Générale peuvent s’inscrire dans le cadre de la théorie des cordes. C’est en étudiant des extensions naturelles de la Relativité Générale que nous pouvons aussi mieux comprendre la théorie d’Einstein. Dans un premier temps, nous exposerons la théorie de la Relativité Générale avec notamment les principes sur lesquelles elle s’appuie et nous donnerons les éléments mathématiques dont nous avons besoin pour la suite. Puis, une première extension sera présentée avec l’introduction de dimensions supplémentaires et de champs de p-formes qui constituent la généralisation naturelle de l’interaction électromagnétique. Nous construirons dans ce cadre de nouvelles solutions statiques de trous noirs où les p-formes permettent de modeler la géométrie de l’horizon. Nous exposerons ensuite l’extension la plus générale de la théorie d’Einstein en dimension quelconque qui génère des équations du second ordre en la métrique : la théorie de Lovelock. Nous déterminerons dans ce contexte une large classe de solutions en dimension 6 pour laquelle la théorie se réduit à celle d’Einstein-Gauss-Bonnet avec toujours la présence de p-formes. Enfin, nous étudierons une généralisation de la Relativité Générale en dimension 4 dont la modification est induite par un champ scalaire couplé conformément à la gravitation. Nous exhiberons notamment une nouvelle solution de trou noir avec un horizon plat dans cette théorie en présence de champs axioniques. Pour clore cette thèse, l’aspect thermodynamique de ces théories gravitationnelles sera étudié ; ce qui permettra de déterminer la masse et les charges de ces nouvelles solutions et d’étudier des phénomènes de transitions de phase en présence d’un champ scalaire conforme. / The main interest of the work exposed in this thesis is to explore hairy black holes in a more general framework than General Relativity by taking into account the presence of a cosmological constant, of higher dimensions, of exotic matter fields or of higher curvature terms. These extensions to General Relativity can be derived in the context of String Theory. It is also by studying natural extensions to General Relativity that we can more deeply understand the theory of Einstein. Firstly, we will display the theory of General Relativity with its building blocks in particular and we will give the mathematical tools that we need afterwards. Then, a first extension will be detailed with the introduction of higher dimensions and p-form fields which constitute the natural generalization of the electromagnetic interaction. We will build in this framework new static black hole solutions where p-form fields allow to shape the geometry of the horizon. Secondly, we will present the general extension of Einstein theory in any dimension which produces second order field equations: Lovelock theory. We will determine in this context a large class of solutions in dimension 6 for which the theory is reduced to Einstein-Gauss-Bonnet theory with the presence of p-form fields. Thirdly, we will study a generalization of General Relativity in dimension 4 whose modification is induced by a conformally coupled scalar field. We will namely exhibit a new black hole solution with a flat horizon in the presence of axionic fields. To conclude this thesis, thermodynamical aspects of these gravitational theories will be studied. In this way, we will be able to determine the mass and the charges of these new solutions and we will examine phase transition phenomena in the presence of a conformally scalar field.

The starting point of any general relativistic numerical simulation is a solution of the Hamiltonian and momentum constraints that (ideally) represents an astrophysically realistic scenario. This dissertation presents a new method to produce initial data sets for binary neutron stars with arbitrary spins and orbital eccentricities. The method only provides approximate solutions to the constraints. However, it was shown that the corresponding constraint violations subside after a few orbits, becoming comparable to those found in evolutions of standard conformally flat, helically symmetric binary initial data. This dissertation presents the first spinning neutron star binary simulations in circular orbits with a orbital eccentricity less then 0.01. The initial data sets corresponding to binaries with spins aligned, zero and anti-aligned with the orbital angular momentum were evolved in time. These simulations show the orbital “hang-up” effect previously seen in binary black holes. Additionally, they show orbital eccentricities that can be up to one order of magnitude smaller than those found in helically symmetric initial sets evolutions. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2013.

Nesta dissertação discutimos o processo da acreção de materia sobre objetos compactos em suas diferentes abordagens. Iniciando com o caso clássico, estudamos sua contraparte relativística e, por fim, investigamos a acreção de fluidos cosmológicos (energia escura e matéria escura) em buracos negros. Devido a simetria esférica adotada, a formação dos chamados discos de acréscimo é proibida (tanto no caso clássico quanto no relativístico) e, portanto, os problemas relacionados com a física dos discos (sua formação e evolução) não foram investigados. No contexto clássico, analisamos inicialmente a chamada acreçao de Bondi, onde o fluido acretado obedece a uma equação de estado politropica e o processo de acreção é descrito pela hidrodinâmica euleriana. A existância de 6 tipos possíveis de solucões para o campo de velocidades é identicada e suas consequências fsicas são discutidas em detalhe. Apenas uma dessas soluções descreve de forma fisicamente consistente o processo de acreção. A taxa de materia acretada é constante, um resultado esperado devido a hipotese de regime estacionário. O estudo do caso relativstico é completamente baseado na Teoria da Relatividade Geral, com o campo gravitacional do corpo central sendo descrito pela metrica de Schwarzschild. O processo relativstico também ocorre sob condições estacionárias e, portanto, a taxa de acreção resultante também é constante. Uma atenção especial foi dedicada para a acreção de fluidos cosmologicos satisfazendo uma equação de estado linear e tambem para o chamado gás de Chaplygin. Estudamos separadamente o comportamento espacial do fluido na região dominada pela acreção e também a influência da evolução cosmologica nas regiões mais distantes. Mostramos que a massa do buraco negro central pode apresentar uma evolução no tempo em escala cosmológica. Os resultados de Babichev (caso linear) e o gás de Chaplygin foram unicadamente descritos através de uma equacão de estado generalizada. Por fim, determinamos também sob que condições a acreção de matéria pode provocar mudancas significativas na massa do buraco negro. / In this dissertation the matter accretion process upon compact objects is discussed in its diferent approaches. Starting with the classical case, the relativistic type was studied and, in the end, the accretion of cosmological fluids (dark energy and dark matter) onto a black hole is investigated. Due to spherical symmetry adopted, the formation of accretion disks is forbidden (both in the classical and relativistic case) and, thus, the problems related to disk physics (the formation and evolution) were not investigated. On the classical approach, the so called Bondi accretion is examined, in which the matter flux occurs according to a polytropic equation of state and the accretion itself is described by the Eulerian hydrodynamic. The existence of 6 possible families of solutions for the velocity field is identied and its physical consequences are thoroughly discussed. Only one of these solutions describes the accretion process in a physically consistent manner. The mass accretion rate is found to be constant, as expected duo to the steady-state hypothesis. The relativistic approach is completely based on the General Relativity Theory. In this case, the gravitational field of the central body is described by the Schwarzschild metric. The relativistic process also occurs in steady-state conditions and, therefore, the accretion flux also is constant. A particular interest is given to the accretion of cosmological fluids with a linear equation of state and of Chaplygin gas. Both the spacial behaviour of the fluids in the accretion dominated region and their cosmological evolution in farther regions are looked into individually. The mass of the central black hole\'s evolution is shown to occur in cosmological times. The Babichev (linear equation of state) and Chaplygin results were unied through a generalised equation of state. At last, it is also determined under which conditions the accretion of cosmological fluids can have astonishing effects on the black hole\'s mass.

Estudamos a evolução temporal de perturbações escalares na vizinhança de uma estrela com densidade uniforme que colapsa em um buraco negro. O trabalho começa com um estudo básico de gravitação e modos quasi-normais. O objetivo principal é resolver a equação de Klein-Gordon sem massa para a perturbação escalar, cuja solução depende de métodos numéricos. Com este objetivo, tratamos os aspectos teóricos de buracos negros e estrelas a partir da solução prevista pela Relatividade Geral para um buraco negro, estrelas com densidade uniforme e estrelas em colapso. Estudamos também uma maneira de reduzirmos a Equação de Klein-Gordon para uma forma conveniente de ser integrada, assim como os métodos numéricos necessários para resolver essa equação. Encontramos soluções para os modos variando a massa M, o raio inicial R e o rótulo do momento angular l. Essas soluções são irregulares em muitas situações, mas em geral elas são crescentes, de acordo com o comportamente observado de explosões de Supernovas. / This work is a study on the time evolution of scalar perturbations around a star collapsing to a black hole. It starts with a basic study of gravitation and quasi-normal modes. The aim is to derive the solution of the massless Klein-Gordon equation, that depends on numerical methods. Aiming at this goal, we studied theoretical aspects of stars, black holes and gravitational collapse. The methods include coordinate substitutions to modify the Klein-Gordon equation to a simple form. We also studied numerical methods for partial differential equations. Solutions of the quasi-normal modes were found with different values of M, R and l. The solutions are irregular in several situations, but some of them display increasing modes, that could be explained by the explosive behavior of Supernovas.

Obtivemos famílias de soluções estáticas e esfericamente simétricas para buracos negros numa brana com vácuo, constante cosmológica não nula e imersa num bulk 5-dimensional assintoticamente anti-de Sitter. Para o caso das geometrias assintoticamente de Sitter, o único membro da família obtida foi a geometria Schwarzschild-de Sitter extrema. Para o caso de geometrias assintoticamente anti-de Sitter, obtivemos toda uma família de soluções, onde cada elemento desta família é determinado por uma constante C. Estudamos o comportamento destas soluções próximo e longe do horizonte de eventos. A seguir, analisamos a evolução de um campo escalar não massivo no exterior dos buracos negros obtidos. Verificamos analiticamente e numericamente o comportamento do potencial efetivo em função da coordenada tartaruga próximo ao horizonte de eventos. Para qualquer geometria ou solução desta família observamos que o campo escalar não massivo decai com o tempo, e o tipo de decaimento depende do valor da constante C. Assim, toda a família de soluções obtida mostrou-se estável. / We found classes of static and spherically symmetric black hole solutions on the brane for a vacuum configuration, non-null cosmological constant, embedded into a 5-dimensional asymptotically anti-de Sitter bulk. In the asymptotically de Sitter case, the only solution obtained was the extreme Schwarzschild-de Sitter geometry. In the asymptotically anti-de Sitter case, a class of solutions was obtained where a particular geometry is fixed by a constant, C. We studied the behaviour of these solutions near and far from the horizon. Next, we studied the time evolution of a scalar field outside the black hole. For the effective potential as function of tortoise coordinate, the analytical results near the horizon agree with numerical calculations. The scalar field decays with time and the particular form of decay depends of the value for C. Thus, all solutions in the obtained class are stable.

Esta tese visa realizar um estudo acerca das freqüências quasinormais das p-branas negras utilizando um campo escalar de teste. No contexto da correspondência AdS/CFT estudamos alguns aspectos da formação de estados supercondutores na teoria de campos definida na borda do espaço-tempo de Gauss-Bonnet AdS d-dimensional. Apresentamos a derivação das soluções das p-branas negras, bem como a análise de sua estrutura causal. Revisamos o regime perturbativo da Relatividade Geral e a interpretação dos modos quasinormais de um buraco negro em termos dos elementos que compõem a correspondência AdS/CFT. Estudamos a evolução de um campo escalar sem massa na geometria das p-branas negras em detalhe, sendo que utilizamos o método semianalítico WKB e a integração característica (Problema de Goursat) para calcular as freqüências quasinormais correspondentes. Por fim, apresentamos uma expressão aproximada de um estado supercondutor na teoria de campos definida na borda do buraco negro de Gauss-Bonnet AdS através do dicionário AdS/CFT. / This thesis aims at studying the quasinormal frequencies of black p-branes using a scalar field in the probe limit. In the context of AdS/CFT correspondence we study some aspects regarding the formation of superconductor states in the field theory set on the AdS boundary of the Gauss-Bonnet AdS spacetime. We present the derivation of black p-brane solutions, as well as the analysis of its causal structure. We review the perturbative regime of General Relativity and the interpretation of the black hole quasinormal modes in terms of the correspondence AdS/CFT. We study the evolution of a massless scalar field in the geometry of black p-branes in detail, and we use the WKB method and the characteristic integration (Goursats problem) in order to calculate the corresponding quasinormal frequencies. Ultimately, we present an approximate expression for a superconductor state in the field theory defined in the AdS boundary of Gauss-Bonnet AdS spacetime.

Nesta dissertação são explorados efeitos clássicos e semi-clássicos em espaços-tempos quase-extremos. Na classe de geometrias tratadas aqui, uma região estática entre dois horizontes é considerada, de forma que estes horizontes estão muito próximos e as suas gravidades superficiais são muito pequenas. Este limite quase-extremo surge em vários contextos de interesse, envolvendo buracos negros assintoticamente de Sitter, buracos de minhoca e buracos negros em universos com seção espacial compacta. No trabalho desenvolvido, buracos de minhoca ligando duas regiões com horizontes cosmológicos são estudados em detalhes. Uma vez caracterizada, algumas das propriedades clássicas destas estruturas e efeitos semi-clássicos são explorados. O tratamento quântico proposto leva naturalmente a uma caracterização termodinâmica associada aos horizontes atrapantes presentes na geometria. Consideramos especificamente propriedades térmicas associadas a um campo escalar nos espaços-tempos de interesse. Uma revisão do formalismo de Hayward é feito, com a sua adaptação para espaços-tempos importantes. Buracos de minhoca no regime quase-extremo são discutidos em detalhes. / In this dissertation, classical and semi-classical effects in quasi-extreme spacetimes are explored. In the class of geometries treated here, a static region between two horizons is considered, in such a way that these horizons are very close and their surface gravities are very small. This quasi-extreme limit appears in several contexts of interest, such as asymptotically de Sitter black holes, wormholes and black holes in universes with compact spatial section. In the developed work, wormholes connecting two regions bounded by cosmological horizons are studied in detail. Once some of the classical properties of these structures are characterized, semi-classical effects are explored. The proposed quantum treatment naturally leads to a thermodynamic characterization associated to the trapping horizons present in the geometry. We specifically consider thermal properties associated to a scalar field in the spacetimes of interest. A review of Hayward\'s formalism is presented, with a proper adaptation to important space-times. Wormholes in the near extreme regime are discussed in detail.