Reentrant phase transitions in Einstein-Maxwell-scalar black holes

Dumitru Astefanesei,Paulina Cabrera,Robert B Mann,Raúl Rojas

doi:10.1103/physrevd.105.046021

Abstract

We consider how scalar fields affect the thermodynamic behavior of charged anti-de Sitter (AdS) black holes. We specifically investigate a class of (3+1)-dimensional exact hairy charged AdS black hole solutions to Einstein-Maxwell-scalar gravity, whose stable ground state and finite horizon area in the zero temperature limit make it of particular interest. We find that the reverse isoperimetric inequality is satisfied for this class and that there exists an intermediate range of the charge that admits reentrant phase behavior, the first example of this type of phase behavior in (3+1) dimensions in a consistent theory.

Highlights

There is considerable ongoing interest in how scalar fields affect gravitational systems, in asymptotically anti-de Sitter (AdS) spacetimes
We investigate a class of (3 þ 1)-dimensional exact hairy charged AdS black hole solutions to Einstein-Maxwell-scalar gravity, whose stable ground state and finite horizon area in the zero temperature limit make it of particular interest
We find that the reverse isoperimetric inequality is satisfied for this class and that there exists an intermediate range of the charge that admits reentrant phase behavior, the first example of this type of phase behavior in (3 þ 1) dimensions in a consistent theory

Summary

INTRODUCTION

There is considerable ongoing interest in how scalar fields affect gravitational systems, in asymptotically anti-de Sitter (AdS) spacetimes. We present the first example of reentrant phase transitions in four spacetime dimensions and in a consistent theory describing a class of exact hairy charged AdS black hole solutions to EinsteinMaxwell-scalar gravity. These are of particular interest because they have finite horizon area in the zero temperature limit [27], whereas without the dilaton potential, these solutions are singular. The dilaton potential of the theory corresponds to an extended supergravity model with dyonic Fayet-Iliopoulos terms and so has a well-defined (stable) ground state [29,30] Such solutions are important in considering quantum phase transitions [31,32] and merit further investigation since the dilaton potential modifies the “AdS box,” suggesting unexpected new features and possible insight into distinct holographic phases of matter [33]. There is an intermediate range of charge for which, as pressure increases, these black holes go from exhibiting no distinguishable phases, to a sequence of reentrant phase transitions, to a standard first-order van der Waals phase transition, to a critical point, to a state where there are again no distinguishable phases

EXTENDED THERMODYNAMICS AND THE REVERSE ISOPERIMETRIC INEQUALITY

DISCUSSION