A unified picture of phase transition: from liquid-vapour systems to AdS black holes

Abstract

Based on fundamental concepts of thermodynamics we examine phase transitions in black holes defined in Anti-de Sitter (AdS) spaces. The method is in line with that used a long ago to understand the liquid-vapour phase transition where the first order derivatives of Gibbs potential are discontinuous and Clausius-Clapeyron equation is satisfied. The idea here is to consider the AdS black holes as grand-canonical ensembles and study phase transition defined by the discontinuity of second order derivatives of Gibbs potential. We analytically check that this phase transition between the 'smaller' and 'larger' mass black holes obey Ehrenfest relations defined at the critical point and hence confirm a second order phase transition. This include both the rotating and charged black holes in Einstein gravity.

Phase transitions of hairy black holes in massive gravity and thermodynamic behavior of charged AdS black holes in an extended phase space

“…These critical exponents of the hairy black hole correspond to the Van der Waals fluid. Now, we are in a position to calculate the critical exponents by using a different method described in [33][34][35] near the critical point. Let us consider the critical exponent α.…”

“…The RN-AdS black hole experiences just a second order phase transition, while Λ is not considered as a thermodynamic pressure in the grand canonical ensemble [33]. Here, we investigate the thermodynamic behavior of Gauss-Bonnet-AdS black holes in the grand canonical ensemble.…”

“…These properties motivated us to investigate the resemblance between the critical behavior of these black holes and that of the Van der Waals fluid [24][25][26][27][28][29][30][31][32]. Also, we computed the critical exponents by using two different methods described in [24,25,[33][34][35][36].…”

Analytical and exact critical phenomena ofd-dimensional singly spinning Kerr-AdS black holes

“…In the grand canonical ensemble with fixed electric potential, there also exists the Hawking-Page phase transition. However, in the canonical ensemble with fixed charge, 1/T -r h displays an oscillatory behavior and the free energy exhibits a swallow tail behavior, which confirms a small/large black hole phase transition reminiscent of a liquid/gas transition of the van der Waals (vdW) fluid [6][7][8][9]. At the critical point, the phase transition will become a second-order one.…”

A unified thermodynamic picture of Hořava-Lifshitz black hole in arbitrary space time

“…In classical thermodynamics first order phase transitions satisfy Clausius-Clapeyron equation, while second order phase transitions satisfy Ehrenfest equations. Recently Banerjee et al [53][54][55][56][57][58] developed a new scheme to study the phase transition in black holes based on Ehrenfest equations by considering the analogy between thermodynamic variables and black hole parameters. This Ehrenfest scheme provides a unique way to classify the nature of phase transitions in black hole systems.…”