Black holes in cosmological spacetimes and alternative theories of gravity

Abstract

This thesis is dedicated to the study of spacetimes surrounding black holes within the context of cosmology, high energy physics and modified theories of gravity. We do this by applying and adapting modern numerical relativity techniques to probe the inhomogeneous and strong field regime in a number of different scenarios. The first application we consider is the nonlinear evolution of unstable flux compactifi- cations in a low-energy limit of string theory. Going beyond stationary solutions and their perturbations, we find rich dynamics, in some cases finding that the evolution from an unstable homogeneous state to a stable warped compactification can serve as a toy-model for slow-roll inflation, while in other cases finding solutions that eventually evolve to a singular state. We then apply the methods for numerically evolving scalar fields coupled to the Ein- stein field equations to address several problems in early universe cosmological scenarios. We study the conditions under which inflation can arise from very inhomogeneous initial conditions. To do so, we introduce and compare several different ways of constucting ini- tial data with large inhomogeneities in both the scalar field and time derivative profiles, by solving for the coupled Einstein constraint equations. We then study the evolution of various classes of initial conditions in both single- and two-field inflationary models. In some of the cases studied, the initial gradient and kinetic energy are much larger than the inflationary energy scale such that black holes can form. Taken together, our results suggest inflation can arise from highly inhomogeneous conditions. Using the same numerical techniques, we study the nonlinear classical dynamics and evo- lutions of black holes in a particular nonsingular bouncing cosmology. We find that for sufficiently large black holes the black hole apparent horizon can disappear during the contraction phase. Despite this, we show that most of the local cosmological evolution remains largely unaffected by the presence of the black hole. For all the cases explored, the black hole’s event horizon persists throughout the bounce, suggesting the nonsingular bouncing model under study is fairly robust to large perturbations. Finally, we use and further develop a novel formulation of the Einstein field equations for evolving a large class of modified theories of gravity. We use this formulation to study the nonlinear dynamics of binary black hole mergers in a specific class of theories, where the black holes acquire a scalar charge. We consider quasi-circular inspirals with different mass-ratios, varying the coupling parameter introducing deviations from General Relativity and quantifying the impact on the emitted scalar and gravitational waveforms. We also compare our numerical results to analytic post-Newtonian calculations of the radiation emitted during the inspiral.