Anti-de Sitter black holes in gauged supergravity. Supergravity flow, thermodynamics and phase transitions

Abstract

This thesis is devoted to the analysis of asymptotically Anti-de Sitter (AdS) black holes arising as solutions of theories of gauged Supergravity in four spacetime dimensions. After a brief recap of the main features of gauged supergravity, the first part of the thesis deals with the explicit construction of solutions and the analysis of the Supergravity flow equations in Fayet-Iliopoulos N=2 gauged supergravity . First of all we analyze the known examples of static supersymmetric extremal Anti-de Sitter black hole solutions in this theory. Then we provide techniques to generalize these solutions to extremal non-supersymmetric ones, found by solving a set of first order equations. Subsequently we find nonextremal solutions, namely black holes with nonvanishing temperature. These configurations are found by solving the full system of the Maxwell-Einstein-scalar equations of motion. We finally make new steps towards a systematic approach to find the most general black hole solution in Fayet-Iliopoulos gauged supergravity. Configurations found by this procedure have nonvanishing angular momentum, electric and magnetic charge, mass and NUT charge. In the second part of the thesis we focus on the nonextremal AdS static solutions and we study the thermodynamics of these configurations. We compute the conserved charges of the solutions and we show that the first law of thermodynamics holds. In the canonical ensemble we discover a first order phase transition between small, hairy black holes and large, less-hairy ones, when the charge is below a critical value. We analyze this phase transition in the dual field theory via the AdS/CFT correspondence, and we find that the process can be interpreted as a liquid-gas phase transition in the dual field theory, that falls in the class of ABJM models. Furthermore we provide some details about the thermodynamics of the rotating configurations. We then compare the various definition of mass for asymptotically Anti-de Sitter configurations. We compute the mass with the Ashtekar-Magnon-Das procedure and by means of holographic renormalization techniques. We provide a set of first order equations for nonextrema static configurations by a suitable squaring of the one-dimensional reduced action. Finally we also provide the correct BPS bound for stationary configurations. We conclude the thesis with further remarks and possible directions of future research.