We present axisymmetric hydrodynamical simulations of the long-term accretion of a rotating gamma-ray burst progenitor star, a "collapsar," onto the central compact object, which we take to be a black hole. The simulations were carried out with the adaptive mesh refinement code FLASH in two spatial dimensions and with an explicit shear viscosity. The evolution of the central accretion rate exhibits phases reminiscent of the long GRB [gamma]-ray and X-ray light curve, which lends support to the proposal by Kumar et al. (2008a,b) that the luminosity is modulated by the central accretion rate. In the first "prompt" phase, the black hole acquires most of its final mass through supersonic quasiradial accretion occurring at a steady rate of [scientific symbols]. After a few tens of seconds, an accretion shock sweeps outward through the star. The formation and outward expansion of the accretion shock is accompanied with a sudden and rapid power-law decline in the central accretion rate Ṁ [proportional to] t⁻²̇⁸, which resembles the L[subscript x] [proportional to] t⁻³ decline observed in the X-ray light curves. The collapsed, shock-heated stellar envelope settles into a thick, low-mass equatorial disk embedded within a massive, pressure-supported atmosphere. After a few hundred seconds, the inflow of low-angular-momentum material in the axial funnel reverses into an outflow from the thick disk. Meanwhile, the rapid decline of the accretion rate slows down, which is potentially suggestive of the "plateau" phase in the X-ray light curve. We complement our adiabatic simulations with an analytical model that takes into account the cooling by neutrino emission and estimate that the duration of the prompt phase can be ~ 20 s. The model suggests that the steep decline in GRB X-ray light curves is triggered by the circularization of the infalling stellar envelope at radii where the virial temperature is below 10¹⁰ K, such that neutrino cooling is inefficient and an outward expansion of the accretion shock becomes imminent; GRBs with longer prompt [gamma]-ray emission should have more slowly rotating envelopes. / text

Current research is focussed on extending our knowledge of how gravity behaves on small scales and near black hole horizons, with various modifications which may probe the low energy limits of quantum gravity. This thesis is concerned with such modifications to gravity and their implications. In chapter two thermodynamical stability analyses are performed on higher dimensional Kerr anti de Sitter black holes. We find conditions for the black holes to be able to be in thermal equilibrium with their surroundings and for the background to be stable against classical tensor perturbations. In chapter three new spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti de Sitter or de Sitter interior and a Schwarzschild (anti) de Sitter or Reissner Nordstrom exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviors of the equation of state for these parameters. In chapter four a six dimensional warped brane world compactification of the Salam-Sezgin supergravity model is constructed by generalizing an earlier hybrid Kaluza Klein / Randall Sundrum construction. We demonstrate that the model reproduces localized gravity on the brane in the expected form of a Newtonian potential with Yukawa type corrections. We show that allowed parameter ranges include values which potentially solve the hierarchy problem. The class of solutions given applies to Ricci flat geometries in four dimensions, and consequently includes brane world realisations of the Schwarzschild and Kerr black holes as particular examples. Arguments are given which suggest that the hybrid compactification of the Salam Sezgin model can be extended to reductions to arbitrary Einstein space geometries in four dimensions. This work furthers our understanding of higher dimensional general relativity, which is potentially interesting given the possibility that higher dimensions may become observable at the TeV scale, which will be probed in the Large Hadron Collider in the next few years.

General relativity has been tested by many experiments, which, however, almost exclusively probe weak spacetime curvatures. In this thesis, I create two frameworks for testing general relativity in the strong-field regime with observations of black holes in the electromagnetic spectrum using current or near-future instruments. In the first part, I design tests of the no-hair theorem, which uniquely characterizes the nature of black holes in terms of their masses and spins in general relativity and which states that these compact objects are described by the Kerr metric. I investigate a quasi-Kerr metric and construct a Kerr-like spacetime, both of which contain an independent parameter in addition to mass and spin. If the no-hair theorem is correct, then any deviation from the Kerr metric has to be zero. I show that already moderate changes of the deviation parameters in either metric lead to significant modifications of the observed signals. First, I apply this framework to the imaging of supermassive black holes using very-long baseline interferometry. I show that the shadow of a black hole as well as the shape of a bright and narrow ring surrounding the shadow depend uniquely on its mass, spin, inclination, and the deviation parameter. I argue that the no-hair theorem can be tested with observations of the supermassive black hole Sgr A*. Second, I investigate the potential of quasi-periodic variability observed in both galactic black holes and active galactic nuclei to test the no-hair theorem in two different scenarios. Third, I show that the profiles of relativistically broadened iron lines emitted from the accretion disks of black holes imprint the signatures of deviations from the Kerr metric. In the second part, I devise a method to test the predicted evaporation of black holes in the Randall-Sundrum model of string theory-inspired braneworld gravity through the orbital evolution of black-hole X-ray binaries and obtain constraints on the size of the extra dimension from A0620-00 and XTE J1118+480. I predict the first detection of orbital evolution in a black-hole binary.

In the following thesis, I will conduct a thermodynamic analysis of the Taub-NUT spacetime in various dimensions, as well as show uses for Taub-NUT and other Hyper-Kahler spacetimes. <br /><br /> Thermodynamic analysis (by which I mean the calculation of the entropy and other thermodynamic quantities, and the analysis of these quantities) has in the past been done by use of background subtraction. The recent derivation of the (A)dS/CFT correspondences from String theory has allowed for easier and quicker analysis. I will use Taub-NUT space as a template to test these correspondences against the standard thermodynamic calculations (via the N&ouml;ether method), with (in the Taub-NUT-dS case especially) some very interesting results. <br /><br /> There is also interest in obtaining metrics in eleven dimensions that can be reduced down to ten dimensional string theory metrics. Taub-NUT and other Hyper-Kahler metrics already possess the form to easily facilitate the Kaluza-Klein reduction, and embedding such metrics into eleven dimensional metrics containing M2 or M5 branes produces metrics with interesting Dp-brane results.

The Event Horizon Telescope (EHT) is a millimeter-wavelength, very-long-baseline interferometry (VLBI) experiment that is capable of observing black holes with horizon-scale resolution. Early observations have revealed variable horizon-scale emission in the Galactic Center black hole, Sagittarius. A* (Sgr A*). Comparing such observations to time-dependent general relativistic magnetohydrodynamic (GRMHD) simulations requires statistical tools that explicitly consider the variability in both the data and the models. We develop here a Bayesian method to compare time-resolved simulation images to variable VLBI data, in order to infer model parameters and perform model comparisons. We use mock EHT data based on GRMHD simulations to explore the robustness of this Bayesian method and contrast it to approaches that do not consider the effects of variability. We find that time-independent models lead to offset values of the inferred parameters with artificially reduced uncertainties. Moreover, neglecting the variability in the data and the models often leads to erroneous model selections. We finally apply our method to the early EHT data on Sgr A*.

Significant X-ray variability and flaring has been observed from Sgr A* but is poorly understood from a theoretical standpoint. We perform general relativistic magnetohydrodynamic simulations that take into account a population of non-thermal electrons with energy distributions and injection rates that are motivated by PIC simulations of magnetic reconnection. We explore the effects of including these non-thermal electrons on the predicted broadband variability of Sgr A* and find that X-ray variability is a generic result of localizing non-thermal electrons to highly magnetized regions, where particles are likely to be accelerated via magnetic reconnection. The proximity of these high-field regions to the event horizon forms a natural connection between IR and X-ray variability and accounts for the rapid timescales associated with the X-ray flares. The qualitative nature of this variability is consistent with observations, producing X-ray flares that are always coincident with IR flares, but not vice versa, i.e., there are a number of IR flares without X-ray counterparts.

We report on the diversity in quasar spectra from the Baryon Oscillation Spectroscopic Survey. After filtering the spectra to mitigate selection effects and Malmquist bias associated with a nearly flux-limited sample, we create high signal-to-noise ratio composite spectra from 58,656 quasars (2.1 <= z <= 3.5), binned by luminosity, spectral index, and redshift. With these composite spectra, we confirm the traditional Baldwin effect (BE, i. e., the anticorrelation of C IV equivalent width ( EW) and luminosity) that follows the relation W-lambda alpha L-beta w with slope beta(w) = -0.35 +/- 0.004, -0.35 +/- 0.005, and -0.41 +/- 0.005 for z. =. 2.25, 2.46, and 2.84, respectively. In addition to the redshift evolution in the slope of the BE, we find redshift evolution in average quasar spectral features at fixed luminosity. The spectroscopic signature of the redshift evolution is correlated at 98% with the signature of varying luminosity, indicating that they arise from the same physical mechanism. At a fixed luminosity, the average C IV FWHM decreases with increasing redshift and is anti-correlated with C IV EW. The spectroscopic signature associated with C IV FWHM suggests that the trends in luminosity and redshift are likely caused by a superposition of effects that are related to black hole mass and Eddington ratio. The redshift evolution is the consequence of a changing balance between these two quantities as quasars evolve toward a population with lower typical accretion rates at a given black hole mass.

In this thesis we study a test electromagnetic field in the vicinity of Kerr black hole and with methods of extraction of its rotational energy. We are investigating a process in which a particle moves in an electromagnetic resonator around Kerr black hole. The energy of the particle is transferred to the electromagnetic field and the particle falls into the black hole with negative energy. We begin with the derivation of Maxwell's and Teukolsky equations and their numerical solutions. We derive a boundary condition for an electromagnetic field on a spherical mirror around the black hole, find the field that satisfies this condition, and describe the procedure for numerical calculation. Next, we calculate the trajectories of charged test particles in such a field and find particles that fall into the black hole with negative energy. We have found that it is possible for the particle to fall into the black hole with the energy of −124% of its rest mass, and the parameters of the electromagnetic field and trajectory of the particle need to be carefully selected.

In this thesis we study a deformation of a black-hole spacetime due to another strong sources of gravity. Keeping within static and axially symmetric metrics, we consider a binary of Schwarzschild black holes held apart from each other by a repulsive effect of an Appell ring. After verifying that such a system can rest in static equilibrium (without any supporting struts), we compute its several basic geometric characteristics and we plot simple invariants determined by the metric functions (especially lapse, or, equivalently, potential) and by their first and second derivatives (gravitational acceleration and Kretschmann scalar). Then we extend the analysis below the black-hole horizon and inspect the behaviour of the scalars inside. The geometry turns out to be deformed in a non-trivial way, we even find regions of negative Kretschmann scalar in some cases. In the second part, we present a summary of the perturbative solution describing a slowly rotating system of a black hole surrounded by a thin finite circular disc, and an analysis of equatorial circular geodesics in such a spacetime. 1

The work is divided into three main parts. In a first time (chapter 1) we define a “BTZ” black hole in anti de Sitter space in any dimension. That will be done by means of group theoretical and symmetric spaces considerations. A physical “good domain” is identified as an open orbit of a subgroup of the isometry group of anti de Sitter. Then (chapter 2) we show that the open orbit is in fact isomorphic to a group (we introduce the notion of globally group type manifold) for which a quantization exists. The quantization of the black hole is performed and its Dirac operator is computed. The third part (appendix A and B) exposes some previously known results. Appendix A is given in a pedagogical purpose: it exposes generalities about deformation quantization and careful examples with SL(2,R), and split extensions of Heisenberg algebras. Appendix B is devoted to some classical results about homogeneous spaces and Iwasawa decompositions. Explicit decompositions are given for every algebra that will be used in the thesis. It serves to make the whole text more self contained and to fix notations. Basics of quantization by group action are given in appendix A.4. One more chapter is inserted (chapter 3). It contains two small results which have no true interest by themselves but which raise questions and call for further development. We discuss a product on the half-plane or, equivalently, on the Iwasawa subgroup of SL(2,R), due to A. Unterberger. We show that the quantization by group action machinery can be applied to this product in order to deform the dual of the Lie algebra of that Iwasawa subgroup. Although this result seems promising, we show by two examples that the product is not universal in the sense that even the product of compactly supported functions cannot be defined on AdS2 by the quantization induced by Unterberger's product. Then we show that the Iwasawa subgroup of SO(2,n) (i.e. the group which defines the singularity) is a symplectic split extension of the Iwasawa subgroup of SU(1,1) by the Iwasawa subgroup of SU(1,n). A quantization of the two latter groups being known, a quantization of SO(2,n) is in principle possible using an extension lemma. Properties of this product and the resulting quantization of AdSl were not investigated because we found a more economical way to quantize AdS4 .