Mathcal{P}\u2013v criticality in gauged supergravities

Shou-Long Li,Hong-Da Lyu,Hao Wei,Hua-Kai Deng

doi:10.1140/epjc/s10052-019-6710-y

Abstract

AdS black holes show richer transition behaviors in extended phase space by assuming the cosmological constant and its conjugate quantity to behave like thermodynamic pressure and thermodynamic volume. We study the extended thermodynamics of charged dilatonic AdS black holes in a class of Einstein–Maxwell-dilaton theories that can be embedded in gauged supergravities in various dimensions. We find that the transition behaviors of higher dimensional dilatonic AdS black holes are different from the four dimensional counterparts, and new transition behaviors emerge in higher dimensions. First, there exists a standard Van der Waals transition only in a five dimensional dilatonic AdS black hole with two equal charges. Second, there emerges a new phase transition branch in negative pressure region in six and seven dimensional dilatonic black holes with two equal charges. Third, there emerge transition behaviors in higher dimensional black hole with single charge cases, which are absent in four dimensions.

Highlights

In the transitions mentioned above, the effects of the scalar fields are not considered
There emerge new behaviors in higher dimensions, which are absent in four dimensions
Because the Van der Waals-like behaviors of six and seven dimensional dilatonic anti-de Sitter (AdS) black holes with two equal charges are the same, so we only plot the P–v diagram with N = 2 of the six dimensional charged dilatonic AdS black hole, which is given by Fig. 2

Summary

Introduction

In the transitions mentioned above, the effects of the scalar fields are not considered. There are many different EMD theories due to different dilaton coupling constants and scalar potentials, and phase transitions are studied in these theories, e.g. in [23–25]. While EM theories can be embedded in string and M-theory in four and five dimensions only, charged dilatonic AdS black holes in gauged supergravities [28–31] can be embedded in higher dimensions. [32], there exist different phase transitions for charged dilatonic AdS black holes with different dilaton coupling constants in EMD theory with a stringinspired potential in four dimensions. J. C (2019) 79:201 sional dilatonic AdS black holes with N equal charges have the same transition behaviors as their four dimensional counterparts, and whether there is any new transition behavior emerging in higher dimensions. 3, we study the phase transitions of charged dilatonic AdS black holes in extended phase space of canonical ensemble in various dimensions and dilaton coupling constants.

Thermodynamics of charged dilatonic AdS black holes

P–v criticality

N = 2 cases

N = 1 cases

Conclusions and outlook