In this work we study properties of the higher-dimensional generally rotating black hole space-time so-called Kerr-NUT-(A)dS and the related spaces with the same explicit and hidden symetries as the Kerr-NUT-(A)dS spacetime. First, we search commuta- tivity conditions for classical (charged) observables and their operator analogues, then we investigate a fulfilment of these conditions in the metioned spaces. We calculate the curvature of these spaces and solve the charged Hamilton-Jacobi and Klein-Gordon equations by the separation of the variables for an electromagnetic field, which pre- serves integrability of motion of a charged particle and mutual commutativity of the corresponding operators.

A colisão de buracos negros é uma das fontes mais importantes de ondas gravitacionais e, em geral, a emissão anisotrópica da radiação causa um recuo do objeto final. Este cenário já é conhecido há décadas, mas foi somente com o recente avanço na relatividade numérica que as velocidades finais dos objetos radiantes foram computadas com precisão. Os valores encontrados podem ser altos o suficiente para exercerem um importante papel no crescimento de buracos negros super massivos via coleção de galáxias e na abundância de núcleos galáticos ativos contendo buracos negros. Este é um autêntico efeito da não linearidade de Relatividade Geral e esta tese fornece uma nova metodologia estudar alguns aspectos da dinâmica da colisão de buracos negros. Consideramos o horizonte como uma tela canônica que codifica as informações da evolução temporal do espaço-tempo. Com esta hipótese, fenômenos como o anti-kick, isto é, uma súbita desaceleração do sistema antes de atingir a velocidade final, são explicado em termos da dissipação das deformações do horizonte. Estudamos primeiramente o Espaço-tempo de Robinson-Trautman. Uma das solução mais simples das equações de Einstein, esta métrica nos fornece um poderoso modelo para investigar tanto a perda de massa quanto o recuo do objeto final. Mostramos que, quando as configurações iniciais tem simetria especular, a massa do buraco negro remanescente e a energia irradiada são completamente determinadas pela condição inicial. Com isso, obtemos as expressões analíticas dos resultados numéricos obtidos anteriormente na literatura. Além disto, com o auxilio do método espectral de Galerkin, analisamos o regime não linear das equações envolvidas e verificamos que se pode estimar a velocidade de recuo final com boa precisão a partir de medidas da assimetria da condição inicial. Introduzimos na seqüência a curvatura efetiva como uma medida das deformações intrínsecas ao horizonte. Além de considerar as deformações gerais, ela também inclui as diferenças entre os hemisférios norte e sul. No espaço-tempo de Robinson-Trautman, essa quantidade se correlaciona de uma forma injetora com a velocidade final. Para superar algumas limitações dessa solução, aplicamos o mesmo procedimento nos resultados da simulação numérica de uma colisão head-on. Neste caso, a curvatura efetiva, está na realidade, correlacionada com a aceleração do sistema. Refinamentos e generalizações desta técnica são também discutidos e propostos para trabalhos futuros. / Colliding black holes are one of the most important sources of gravitational waves and the anisotropic emission of the radiation generally causes the recoil of the final hole. This scenario has been known for decades, but it is only thanks to the recent progress in numerical relativity that the final velocity have been accurately computed. The values found can be large enough to play an important role in the growth of supermassive black holes via mergers of galaxies and on the number of galaxies containing them. This is a genuine nonlinear effect of general relativity and this thesis provides a new methodology to study some features on the dynamics of the collision. We propose that the horizon is a canonical screen, which encodes he information of its surroundings. With this assumption, phenomena such as the anti-kick, namely the sudden deceleration before reaching the final velocity, are explained in terms of the dissipation of the horizons deformation. We first study the Robinson-Trautman spacetime. One of the simplest solutions of Einsteins equations, it provides us with a powerful toymodel to investigate both the mass loss of the system and the recoil of the final object. We show that, for the case of reflectionsymmetric initial configurations, the mass of the remnant black-hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some numerical results that had appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the non-linear regime of the equations involved, we found that the recoil velocity can be estimated with good accuracy from some symmetry measures of the initial data. Then we introduce the effective urvature as a measure of intrinsic deformations on the horizon. Not only does it account for overall deformation, but also for the differences on the north and south hemispheres. In the Robinson-Trautman spacetime, this quantity correlates in an injective way with the final velocity. To overcome some caveats of this solutions, we apply the same procedure to the results given by numerical simulations of a head-on collision. In the case, the effective curvature is actually correlated with the acceleration of the system. Further improvement and generalizations of this technic is also discussed and proposed for future work.

Marginally outer-trapped surfaces (MOTSs) are found for a family of space-like hypersurfaces described by the Brill-Lindquist initial data. These hypersurfaces contain a singular ring characterized by its radius, mass and charge. Due to the ring character of the singularity, these surfaces are natural candidates for MOTSs with toroidal topology. By adjusting and employing the numerical method of geodesics, we indeed localize MOTSs of both spherical and toroidal topology, and compare the results with those obtained previously by Jaramillo & Lousto.

En 1916 Albert Einstein énonce la théorie de la relativité : véritable révolution scientifique du XXe siècle, elle aura des répercussions touchant à tous les domaines de la connaissance. L'objectif de notre étude est de tracer un cadre des relations existantes entre la littérature européenne et la théorie de la relativité, sur l'interaction de leurs deux langues et sur l'échange de leurs images. Si la science et la littérature dialoguent entre elles, elles le font au sein d'une atmosphère, l'esprit du temps. Les deux disciplines prennent leurs images et leurs thèmes d'un terroir commun : elles deviennent ainsi l'expression d'une époque et en même temps la source de laquelle l'époque se nourrit. Le dialogue entre science et littérature se traduit dans notre méthodologie : le paradoxe des jumeaux, qu'Einstein utilise pour expliquer la déformation spatio-temporelle, se traduit dans le thème du double à partir duquel on a sélectionné un corpus européen. Ensuite, on a procède à une analyse sur deux niveaux, l'un narratologique et l'autre symbolique. Pour le premier niveau on a analysé l'espace-temps en relation au double : on a vu comment les deux sont entrelacés et comment l'espace-temps ne se limite pas à assumer une fonction de décor. Pour le deuxième niveau d'analyse on a emprunté certaines images utilisées par Einstein dans ses textes de vulgarisation, comme le train et la lumière, pour construire une grille critique que nous avons appelé « constellation einsteinienne ». Grace à cette grille de symboles, qui se superpose à celle narratologique, nous pouvons voir comme les éléments évoqués par Einstein se transforment en littérature en gardant toute leur valeur scientifique. De notre analyse résulte un cadre où des éléments scientifiques et des textes de fiction s'entrelacent dans l'expression de l'esprit du temps. La relativité scientifique trouve son contrepartie dans la relativité littéraire. / In 1916 Albert Einstein formulated the theory of relativity, a great XX century scientific revolution, which will have repercussions affecting all areas of human knowledge. The aim of our study is to draw a framework of the existing relations between European literature and the theory of relativity, about the interaction of their two languages and the exchange of their images. If science and literature interact to each other, they do so within an atmosphere, the spirit of the times. The two disciplines take their images and their themes from a common ground: they thus become the expression of an era and at the same time the source from which the era nourishes itself. The dialogue between science and literature is reflected in our methodology: the paradox of twins, which Einstein uses to explain spatio-temporal deformation, is transformed in the double theme from which a European corpus was selected. Then, we proceeded to an analysis on two levels, the one narratological and the other symbolic. For the first level, we have focused on space-time double relation, discovering how the two are interlaced and how space-time is not limited to assuming a decor function. For the second level of analysis we have borrowed certain images used by Einstein in his popularization texts, such as train and light, to build a critical grid that we have called the “Einsteinian constellation”. Thanks to this grid of symbols, which is superimposed on that of narratology, we can see that the elements evoked by Einstein transform into literature while retaining all their scientific value. From our analysis results a framework where scientific elements and fiction texts intertwine in the expression of the spirit of the time. Scientific relativity finds its counterpart in literary relativity.

[Truncated abstract] As gravitational wave detectors approach sensitivities that will allow observations to become routine, astrophysics lies on the cusp of an exciting new era. Potential sources will include transients such as merging neutron stars and black holes, supernova explosions or the engines that power gamma-ray bursts. This thesis will be devoted to the astrophysical gravitational wave background signal produced by cosmological populations of such transient signals. Particular attention will be devoted to the observation-time dependence imposed on the individual sources that accumulate to produce a gravitational wave background signal. The ultimate aim is to determine what information is encoded in the temporal evolution of such a signal. To lay the foundations for further investigation, the stochastic gravitational wave background signal from neutron star birth throughout the Universe has been calculated. In view of the uncertainties in both the single-source emissions and source rate histories, several models of each are employed. The results show that that the resulting signals are only weakly dependent on the source-rate evolution model and that prominent features in the single-source spectra can be related to the background spectra. In comparison with previous studies, the use of relativistic single-source gravitational wave waveforms rather than Newtonian models and a more slowly evolving source-rate density results in a 1 { 2 order of magnitude reduction in signal. ... A comparison with the more commonly used brightness distribution of events shows that when applying both methods to a data stream containing a background of Gaussian distributed false alarms, the brightness distribution yielded lower standard errors, but was biased by the false alarms. In comparison, a fitting procedure based on the time evolution of events was less prone to errors resulting from false alarms, but as fewer events contributed to the data, had a lower resolution. In further support of the time dependent signature of transient events, an alternative technique is fiapplied to the same source population. In this case, the local rate density is probed by measuring the statistical compatibility of the filtered data against synthetic time dependent data. Although this method is not as compact as the fitting procedure, the rate estimates are compatible. To further investigate how the observation time dependence of transient populations can be used to constrain global parameters, the method is applied to Swift long gamma-ray burst data. By considering a distribution in peak °ux rather than a gravitational wave amplitude, gamma-ray bursts can be considered as a surrogate for resolved gravitational wave transients. For this application a peak °ux{observation time relation is described that takes the form of a power law that is invariant to the luminosity distribution of the sources. Additionally, the method is enhanced by invoking time reversal invariance and the temporal cosmological principle. Results are presented to show that the peak °ux{observation time relation is in good agreement with recent estimates of source parameters. Additionally, to show that the intrinsic time dependence allows the method to be used as a predictive tool, projections are made to determine the upper limits in peak °ux of future gamma-ray burst detections for Swift.

A colisão de buracos negros é uma das fontes mais importantes de ondas gravitacionais e, em geral, a emissão anisotrópica da radiação causa um recuo do objeto final. Este cenário já é conhecido há décadas, mas foi somente com o recente avanço na relatividade numérica que as velocidades finais dos objetos radiantes foram computadas com precisão. Os valores encontrados podem ser altos o suficiente para exercerem um importante papel no crescimento de buracos negros super massivos via coleção de galáxias e na abundância de núcleos galáticos ativos contendo buracos negros. Este é um autêntico efeito da não linearidade de Relatividade Geral e esta tese fornece uma nova metodologia estudar alguns aspectos da dinâmica da colisão de buracos negros. Consideramos o horizonte como uma tela canônica que codifica as informações da evolução temporal do espaço-tempo. Com esta hipótese, fenômenos como o anti-kick, isto é, uma súbita desaceleração do sistema antes de atingir a velocidade final, são explicado em termos da dissipação das deformações do horizonte. Estudamos primeiramente o Espaço-tempo de Robinson-Trautman. Uma das solução mais simples das equações de Einstein, esta métrica nos fornece um poderoso modelo para investigar tanto a perda de massa quanto o recuo do objeto final. Mostramos que, quando as configurações iniciais tem simetria especular, a massa do buraco negro remanescente e a energia irradiada são completamente determinadas pela condição inicial. Com isso, obtemos as expressões analíticas dos resultados numéricos obtidos anteriormente na literatura. Além disto, com o auxilio do método espectral de Galerkin, analisamos o regime não linear das equações envolvidas e verificamos que se pode estimar a velocidade de recuo final com boa precisão a partir de medidas da assimetria da condição inicial. Introduzimos na seqüência a curvatura efetiva como uma medida das deformações intrínsecas ao horizonte. Além de considerar as deformações gerais, ela também inclui as diferenças entre os hemisférios norte e sul. No espaço-tempo de Robinson-Trautman, essa quantidade se correlaciona de uma forma injetora com a velocidade final. Para superar algumas limitações dessa solução, aplicamos o mesmo procedimento nos resultados da simulação numérica de uma colisão head-on. Neste caso, a curvatura efetiva, está na realidade, correlacionada com a aceleração do sistema. Refinamentos e generalizações desta técnica são também discutidos e propostos para trabalhos futuros. / Colliding black holes are one of the most important sources of gravitational waves and the anisotropic emission of the radiation generally causes the recoil of the final hole. This scenario has been known for decades, but it is only thanks to the recent progress in numerical relativity that the final velocity have been accurately computed. The values found can be large enough to play an important role in the growth of supermassive black holes via mergers of galaxies and on the number of galaxies containing them. This is a genuine nonlinear effect of general relativity and this thesis provides a new methodology to study some features on the dynamics of the collision. We propose that the horizon is a canonical screen, which encodes he information of its surroundings. With this assumption, phenomena such as the anti-kick, namely the sudden deceleration before reaching the final velocity, are explained in terms of the dissipation of the horizons deformation. We first study the Robinson-Trautman spacetime. One of the simplest solutions of Einsteins equations, it provides us with a powerful toymodel to investigate both the mass loss of the system and the recoil of the final object. We show that, for the case of reflectionsymmetric initial configurations, the mass of the remnant black-hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some numerical results that had appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the non-linear regime of the equations involved, we found that the recoil velocity can be estimated with good accuracy from some symmetry measures of the initial data. Then we introduce the effective urvature as a measure of intrinsic deformations on the horizon. Not only does it account for overall deformation, but also for the differences on the north and south hemispheres. In the Robinson-Trautman spacetime, this quantity correlates in an injective way with the final velocity. To overcome some caveats of this solutions, we apply the same procedure to the results given by numerical simulations of a head-on collision. In the case, the effective curvature is actually correlated with the acceleration of the system. Further improvement and generalizations of this technic is also discussed and proposed for future work.

Black holes are one of the most interesting objects in the universe, and studying these objects should give exciting results. This research will investigate the General Theory of Relativity, explaining the essence of the theory needed for deriving solutions for a Schwarzschild black hole. This knowledge leads to deriving the equations of motion of a bosonic scalar field around a Schwarzschild black hole. Computing the dynamical evolution of that scalar field, and taking the limit far away from the black hole, gives an approximation derivation of the  Schrödinger equation. This study opens many doors to future research about black holes and scalar fields. / Svarta hål är ett av de mest intressanta objekten i universum, och därför, att studera dessa föremål bör ge spännande resultat.I detta arbete kommer den allmänna relativitetsteorin  att studeras och förklaras med allt som behövs för att härledalösningar för en Schwarzschild svart hål. Denna kunskap leder till att härleda rörelseekvationerna för ett bosoniskt skalärfält runt ett Schwarzschild svart hål.Genom att beräkna den dynamiska utvecklingen av det skalära fältet och ta gränsen långt bort från svarta hålet,så kommer det at ge en approximativ härledning av Schrödinger ekvationen. Den här typen av studier öppnar många dörrar för framtida forskning om svarta hål och skalära fält.

The aim of this work is to derive mathematical descriptions of gravitation. Postulating gravitation as a force field, Newton's law of gravitation is heuristically derived by considering linear differential operators invariant under euclidean isometries and by finding the fundamental solution to Helmholtz equation in three dimensions. Thereafter, the theory of differential geometry is introduced, providing a framework for the subsequent review of gravitation as curvature. Lastly, in the light of Einstein's postulates and equivalence principle, Lovelock's proof of uniqueness of Einstein's field equations is presented.

<p>The properties of neutron stars and black holes are investigated within a class of alternative theories of gravity known as Scalar-Tensor theories, which extend General Relativity by introducing additional light scalar fields to mediate the gravitational interaction.</p> <p>It has been known since 1993 that neutron stars in certain Scalar-Tensor theories may undergo ‘scalarization’ phase transitions. The Weak Central Coupling (WCC) expansion is introduced for the purpose of describing scalarization in a perturbative manner, and the leading-order WCC coefficients are calculated analytically for constant-density stars. Such stars are found to scalarize, and the critical value of the quadratic scalar-matter coupling parameter β_s = −4.329 for the phase transition is found to be similar to that of more realistic neutron star models.</p> <p>The influence of cosmological and galactic effects on the structure of an otherwise isolated black hole in Scalar-Tensor gravity may be described by incorporating the Miracle Hair Growth Formula discovered by Jacobson in 1999, a perturbative black hole solution with scalar hair induced by time-dependent boundary conditions at spatial infinity. It is found that a double-black-hole binary (DBHB) subject to these boundary conditions is inadequately described by the Eardley Lagrangian and emits scalar dipole radiation.</p> <p>Combining this result with the absence of observable dipole radiation from quasar OJ287 (whose quasi-periodic ‘outbursts’ are consistent with the predictions of a general-relativistic DBHB model at the 6% level) yields the bound |φ/Mpl| < (16 days)^-1 on the cosmological time variation of canonically-normalized light (m < 10⁻²³ eV) scalar fields at redshift z ∼ 0.3.</p> / Doctor of Philosophy (PhD)

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: See fulltext for abstract. / AFRIKAANSE OPSOMMING: Sien volteks vir opsomming.