In this thesis we investigate two approaches to quantum gravity. The first is the emergence of gravity from a discrete fundamental theory, and the second is the direct quantisation of gravity. For the first we develop tools to determine with relatively high accuracy the speed of propagation of information in collective modes which ultimately should give us some information about the emergent causal structure. We found a way of finding the dependence on the relative interaction strengths of the Hamiltonian and we also managed to calculate this speed in the case where the operators in the Hamitonian were not necessarily bounded. For the second approach, we investigated the phenomenology of Loop Quantum Gravity. We found that ultra light black holes (lighter than the Planck mass) have interesting new properties on top of being non-singular. First their horizon is hidden behind a Plancksized wormhole, second their specific heat capacity is positive and they are quasi-stable, they take an infinite amount of time evaporate. We investigated the dynamics of their collapse and evaporation explicitly seeing that not only was there no singularity, but there is also no information loss problem. Looking at how primordial black holes were in existence, we found that they might account for a significant portion of dark matter. And if they did, their radiation spectrum is such that the black holes in the dark matter halo of our galaxy could be the source for the ultra high energy cosmic rays we observe on earth.

In this thesis we present a time-dependent multi-zone radiative transfer code and its applications to study the multiwavelength emission of blazars. The multiwavelength variability of blazars is widely believed to be a direct manifestation of the formation and propagation of relativistic jets, and hence the related physics of the black hole - accretion disk - jet system. However, the understanding of these variability demands highly sophisticated theoretical analysis and numerical simulations. Especially, the inclusion of the light travel time effects(LTTEs) in these calculations has long been realized important, but very difficult. The code we use couples Fokker-Planck and Monte Carlo methods, in a 2 dimensional (cylindrical) geometry. For the first time all the LTTEs are fully considered, along with a proper, full, self-consistent treatment of Compton cooling, which depends on the LTTEs. Using this code, we studied a set of physical processes that are relevant to the variability of blazars, including electron injection and escape, radiative cooling, and stochastic particle acceleration. Our comparison of the observational data and the simulation results revealed that a combination of all those processes is needed to reproduce the observed behaviors of the emission of blue blazars. The simulation favors that the high energy emission at quiet and flare stages comes from the same location. We have further modeled red blazars PKS 1510-089. External radiation, which comes from the broad line region (BLR) or infrared torus, is included in the model. The results confirm that external Compton model can adequately describe the emission from red blazars. The emission from BLR is favored as the source of Inverse Compton seed photons, compared to synchrotron and IR torus radiation.

A number of models of nature incorporate dimensions beyond our observed four. In this thesis we examine some examples and consequences of classical instabilities that emerge in the higher-dimensional theories of gravity which can describe their low energy phenomenology. <br /><br /> We first investigate a gravitational instability for black strings carrying momentum along an internal direction. We argue that this implies a new type of solution that is nonuniform along the extra dimension and find that there is a boost dependent critical dimension for which they are stable. Our analysis implies the existence of an analogous instability for the five-dimensional black ring. We construct a simple mode of the black ring to aid in applying these results and argue that such rings should exist in any number of space-time dimensions. <br /><br /> Next we consider a recently constructed class of nonsupersummetric solutions of type IIB supergravity which are everywhere smooth and have no horizon. We demonstrate that these solutions are all classically unstable. The instability is a generic feature of horizonless geometries with an ergoregion. We consider the endpoint of this instability and argue that the solutions decay to supersymmetric configurations. We also comment on the implications of the ergoregion instability for Mathur's 'fuzzball' proposal. <br /><br /> Finally, we consider an interesting braneworld cosmology in the Randall-Sundrum scenario constructed using a bulk space-time which corresponds to a charged AdS black hole. In particular, these solutions appear to 'bounce', making a smooth transition from a contracting to an expanding phase. By considering the space-time geometry more carefully, we demonstrate that generically in these solutions the brane will encounter a singularity in the transition region.

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.

A number of models of nature incorporate dimensions beyond our observed four. In this thesis we examine some examples and consequences of classical instabilities that emerge in the higher-dimensional theories of gravity which can describe their low energy phenomenology. <br /><br /> We first investigate a gravitational instability for black strings carrying momentum along an internal direction. We argue that this implies a new type of solution that is nonuniform along the extra dimension and find that there is a boost dependent critical dimension for which they are stable. Our analysis implies the existence of an analogous instability for the five-dimensional black ring. We construct a simple mode of the black ring to aid in applying these results and argue that such rings should exist in any number of space-time dimensions. <br /><br /> Next we consider a recently constructed class of nonsupersummetric solutions of type IIB supergravity which are everywhere smooth and have no horizon. We demonstrate that these solutions are all classically unstable. The instability is a generic feature of horizonless geometries with an ergoregion. We consider the endpoint of this instability and argue that the solutions decay to supersymmetric configurations. We also comment on the implications of the ergoregion instability for Mathur's 'fuzzball' proposal. <br /><br /> Finally, we consider an interesting braneworld cosmology in the Randall-Sundrum scenario constructed using a bulk space-time which corresponds to a charged AdS black hole. In particular, these solutions appear to 'bounce', making a smooth transition from a contracting to an expanding phase. By considering the space-time geometry more carefully, we demonstrate that generically in these solutions the brane will encounter a singularity in the transition region.

Astrophysical flows have an enormous dynamic range of relevant length scales. The physics occurring on the smallest scales often influences the physics of the largest scales, and vice versa. I present a detailed study of the multiscale and multidimensional behavior of three high-energy astrophysical flows: jet-driven supernovae, massive black hole accretion, and current-driven instabilities in gamma-ray burst external shocks. Both theory and observations of core-collapse supernovae indicate these events are not spherically-symmetric; however, the observations are often modeled assuming a spherically-symmetric explosion. I present an in-depth exploration of the effects of aspherical explosions on the observational characteristics of supernovae. This is accomplished in large part by high-resolution, multidimensional numerical simulations of jet-driven supernovae. The existence of supermassive black holes in the centers of most large galaxies is a well-established fact in observational astronomy. How such black holes came to be so massive, however, is not well established. In this work, I discuss the implications of radiative feedback and multidimensional behavior on black hole accretion. I show that the accretion rate is drastically reduced relative to the Eddington rate, making it unlikely that stellar mass black holes could grow to supermassive black holes in less than a Hubble time. Finally, I discuss a mechanism by which magnetic field strength could be enhanced behind a gamma-ray burst external shock. This mechanism relies on a current-driven instability that would cause reorganization of the pre-shock plasma into clumps. Once shocked, these clumps generate vorticity in the post-shock plasma and ultimately enhance the magnetic energy via a relativistic dynamo process. / text

Isolated and Dynamical horizons are used to generate boundary conditions upon the lapse and shift vectors. Numerous results involving the Hamiltonian of General relativity are derived, including a self-contained derivation of the Hamiltonian equations of general relativity using both a direct 'brute force' method of directly computing Lie derivatives, as well as the standard Hamil- tonian approach. Conclusions are compared to numerous examples, including the Kerr, Schwarzschild-De Sitter, McVittie, and Vaiyda spacetimes. / text

In this thesis we investigate two different aspects of the AdS/CFT correspondence. We first investigate the holographic AdS/CMT correspondence. Gravitational backgrounds in d+2 dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in d+1 dimensions with critical exponent z&gt;1. We numerically explore a dilaton-Einstein-Maxwell model admitting such backgrounds as solutions. We show how to embed these solutions into AdS space for a range of values of z and d. We next investigate the AdS3/CFT2 correspondence and focus on the microscopic CFT description of the D1-D5 system on T^4*S_1. In the context of the fuzzball programme, we investigate deforming the CFT away from the orbifold point and study lifting of the low-lying string states. We start by considering general 2D orbifold CFTs of the form M^N/S_N, with M a target space manifold and S_N the symmetric group. The Lunin-Mathur covering space technique provides a way to compute correlators in these orbifold theories, and we generalize this technique in two ways. First, we consider excitations of twist operators by modes of fields that are not twisted by that operator, and show how to account for these excitations when computing correlation functions in the covering space. Second, we consider non-twist sector operators and show how to include the effects of these insertions in the covering space. Using the generalization of the Lunin-Mathur symmetric orbifold technology and conformal perturbation theory, we initiate a program to compute the anomalous dimensions of low-lying string states in the D1-D5 superconformal field theory. Our method entails finding four-point functions involving a string operator O of interest and the deformation operator, taking coincidence limits to identify which other operators mix with O, subtracting conformal families of these operators, and computing their mixing coefficients. We find evidence of operator mixing at first order in the deformation parameter, which means that the string state acquires an anomalous dimension. After diagonalization this will mean that anomalous dimensions of some string states in the D1-D5 SCFT must decrease away from the orbifold point while others increase. Finally, we summarize our results and discuss some future directions of research.

In this thesis we investigate two different aspects of the AdS/CFT correspondence. We first investigate the holographic AdS/CMT correspondence. Gravitational backgrounds in d+2 dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in d+1 dimensions with critical exponent z&gt;1. We numerically explore a dilaton-Einstein-Maxwell model admitting such backgrounds as solutions. We show how to embed these solutions into AdS space for a range of values of z and d. We next investigate the AdS3/CFT2 correspondence and focus on the microscopic CFT description of the D1-D5 system on T^4*S_1. In the context of the fuzzball programme, we investigate deforming the CFT away from the orbifold point and study lifting of the low-lying string states. We start by considering general 2D orbifold CFTs of the form M^N/S_N, with M a target space manifold and S_N the symmetric group. The Lunin-Mathur covering space technique provides a way to compute correlators in these orbifold theories, and we generalize this technique in two ways. First, we consider excitations of twist operators by modes of fields that are not twisted by that operator, and show how to account for these excitations when computing correlation functions in the covering space. Second, we consider non-twist sector operators and show how to include the effects of these insertions in the covering space. Using the generalization of the Lunin-Mathur symmetric orbifold technology and conformal perturbation theory, we initiate a program to compute the anomalous dimensions of low-lying string states in the D1-D5 superconformal field theory. Our method entails finding four-point functions involving a string operator O of interest and the deformation operator, taking coincidence limits to identify which other operators mix with O, subtracting conformal families of these operators, and computing their mixing coefficients. We find evidence of operator mixing at first order in the deformation parameter, which means that the string state acquires an anomalous dimension. After diagonalization this will mean that anomalous dimensions of some string states in the D1-D5 SCFT must decrease away from the orbifold point while others increase. Finally, we summarize our results and discuss some future directions of research.

In this thesis we investigate two approaches to quantum gravity. The first is the emergence of gravity from a discrete fundamental theory, and the second is the direct quantisation of gravity. For the first we develop tools to determine with relatively high accuracy the speed of propagation of information in collective modes which ultimately should give us some information about the emergent causal structure. We found a way of finding the dependence on the relative interaction strengths of the Hamiltonian and we also managed to calculate this speed in the case where the operators in the Hamitonian were not necessarily bounded. For the second approach, we investigated the phenomenology of Loop Quantum Gravity. We found that ultra light black holes (lighter than the Planck mass) have interesting new properties on top of being non-singular. First their horizon is hidden behind a Plancksized wormhole, second their specific heat capacity is positive and they are quasi-stable, they take an infinite amount of time evaporate. We investigated the dynamics of their collapse and evaporation explicitly seeing that not only was there no singularity, but there is also no information loss problem. Looking at how primordial black holes were in existence, we found that they might account for a significant portion of dark matter. And if they did, their radiation spectrum is such that the black holes in the dark matter halo of our galaxy could be the source for the ultra high energy cosmic rays we observe on earth.