Black Holes and Holography: Insights and Applications

This dissertation focuses on the role classical black hole spacetimes play in the AdS/CFT correspondence. We begin by introducing some of the puzzles surrounding black holes, and we review their connection to strongly correlated CFT states through holography. Additionally, we detail numerical methods for constructing black hole states of non-trivial topology in three dimensions and evaluating their actions.In part I we focus on using black hole spacetimes to derive insights into holography and quantum gravity. Using numerical methods, we study a class of non-local operators in the CFT, defined via a path integral over a torus with two punctures. In particular, we are interested in determining the spectrum of such operators at various points in moduli space. In the dual gravitational theory, such an operator might be used to construct black hole spacetimes with arbitrarily high topology behind the horizon. We present evidence suggesting this fails, and along the way encounter a puzzle related to the positivity of these operators. The resolution of this puzzle lies in developing technology to better catalogue the relevant gravitational phases.Additionally, we use multi-boundary wormhole spacetimes to investigate the constraints on the subregion entanglement entropies of holographic states. We find tension with previously claimed properties of these constraints, namely that they define a polyhedral cone in the space of entanglement entropies. These results either suggest the possible existence of further unknown constraints, or the need for a more complicated construction procedure to realize the extremal states.In part II we focus on the holographic description of CFT states via black hole spacetimes, focusing on spacetimes perturbatively constructed from the planar AdS-Schwarzschild metric. First, we consider corrections to properties of confining ground states of holographic CFTs as we introduce spatial curvature. Next, we compute shifts in vacuum entanglement entropy in a thermal state with a locally varying temperature as well as similar shifts in the confining ground states with spatial curvature