Generalized Thermodynamics and Phase Transitions of Vaidya-adS Black Holes

Abstract

This work investigates the thermodynamics of non-stationary anti-de Sitter (adS) black holes and their gauge-gravity duals. To model a non-equilibrium process, we employ a time-dependent Vaidya-adS metric to describe the collapse of a null fluid and the subsequent thermalization of the dual field theory. We introduce an effective version of free energy as a quasilocal probe to be used in a dynamical setup. By analyzing how this quantity evolves, we show that a first-order phase transition occurs when the final black-hole mass exceeds the limit established by the Hawking-Page temperature. Furthermore, we demonstrate that the final state only approaches the thermal behavior of the N=4 supersymmetric Yang-Mills theory for mass states much larger than the adS radius. Finally, we compute the boundary energy-momentum tensor using holographic renormalization and compare the resulting energy density with the strong-coupling limit. This demonstrates that the dual description provides a consistent framework for both the equilibrium and non-equilibrium thermodynamics of strongly coupled gauge theories.