Probes of Supersymmetric Black Holes in AdS

Abstract

Black holes have emerged as crucial conceptual laboratories for testing ideas towards the development of a quantum theory of gravity, as key black hole properties have been formulated in dual quantum terms using the proposed AdS/CFT correspondence. Supersymmetric black holes in AdS in particular have a rich description on both the gravitational and field-theoretic sides of this duality. In this thesis, we will be studying the stability as well as the spacetime structure of these black holes, and will be probing close to and away from the critical parameters at which these black holes become supersymmetric. There is a lack of a general understanding of generically non-supersymmetric black holes, and the goal of this thesis will be to expand with further quantitative explorations and systematize our understanding in that area.

The first part of this thesis will be a survey of Kerr-Newman-AdS5 black hole thermodynamics, away from and approaching the supersymmetric (BPS) regime. We use that limiting process to define thermodynamics directly on the BPS surface, and are able to parametrize these BPS thermodynamics in terms of a new fugacity. We then find that the free energy in this formulation can be directly mapped to the HHZ free energy obtained from the dual field theory.

The second part of this thesis consists of an in-depth analysis of the black hole solution to N=2 gauged supergravity, in particular the radial profile of its fields from the near-horizon region all the way to asymptotic infinity. We develop the necessary radial flow equations with the help of the N=2 supersymmetric variations, as well as charge conservation laws based on a nontrivial adaptation of the Noether-Wald procedure in gauged supergravity. We are then able to characterize the radial flow of the black hole solution in great detail. Lastly, we connect the near-horizon limit of this flow to the entropy extremization formalism, and give a full description of the supersymmetric extrema of the theory.