Black holes in the gravity/gauge theory correspondence

Abstract

The AdS/CFT correspondence provides a microscopic description of black hole thermodynamics. In this thesis, I study the relation between the classical physics of black holes and this microscopic description. I first consider the gauge theory's holographic encoding of non-trivial global causal structure, by studying various probes of the black hole. I study the charged black hole, so that the thermal scale is separated from the horizon scale, to demonstrate which relates to the field theory scale size. I find that, when probing the horizon, both Wilson loops and the duals of static supergavity probes have a scale size determined by the horizon, but the field theory scale size is divergent for a time-dependent probe. I also use the bulk black hole geometry to study the physics of the boundary theory. If we consider a dynamical boundary, a braneworld cosmology is induced from the bulk. However, the presence of matter on the brane introduces unconventional quadratic terms in the FRW equations of this braneworld. I find that bulk black holes induce identical unconventional terms on a matterless brane, therefore providing an alternative description of the same cosmology. A new conjecture relating classical and thermodynamic stability of black branes has emerged from the AdS/CFT correspondence. I make progress in proving this for the case of Schwarzschild black holes in a finite cavity. I also extend the conjecture to the supergravity backgrounds of the direct product form Schwarzschild-AdS x Sphere, which are relevant to my study of the AdS/CFT correspondence.