Explorations in de Sitter Space and Amorphous Black Hole Bound States in String Theory

Abstract

This dissertation is split into two distinct halves. The first covers various calculations done in order gain insights on holography in de Sitter space. The dispersion relation of linear perturbations of empty de Sitter space are numerically computed as a function of the location of a hypersurface on which conformal Dirichlet boundary conditions are imposed. When the hypersurface is near the south pole, the dispersion relation is linear, whereas for a hypersurface near the cosmological horizon, it satisfies that of the incompressible Navier-Stokes equation. This result is shown to hold for non-linear perturbations. We also compute the thermodynamic stability of rotating black holes in $dS_4$ as a function of their mass and angular momentum. We focus particularly on the rotating Nariai geometry, which is a near horizon limit of the rotating black hole as the outer and cosmological horizons tend towards each other. We study massless scalar fields in these backgrounds and obtain their quasinormal mode spectrum explicitly. We uncover an interesting structure in their two-point functions, namely that they resemble thermal Green's functions of a two-dimensional conformal field theory. The second half of this dissertation deals with the study of multicentered black holes in string theory and their finite temperature extensions. We show that there exist finite temperature single-centered solutions in $\mathcal{N}=2$ supergravity in asymptotically flat space that admit bound states with BPS probe particles. We compute the existence regions of these bound states as well as their dependence on temperature. We embed these solutions in Fayet-Illiopoulos gauged supergravity and show that bound states persist in asymptotically $AdS_4$ spacetimes. We make attempts to understand these disordered bound states as amorphous/glassy phases of the dual conformal field theory.Physic