Range of novel black hole phase transitions via massive gravity: Triple points and N-fold reentrant phase transitions

TL;DR

This paper investigates complex phase transitions of black holes in higher-dimensional massive gravity theories, revealing phenomena like triple points and N-fold reentrant transitions, which could parallel behaviors in condensed matter systems.

Contribution

It uncovers new types of phase transitions, including triple points and N-fold reentrant transitions, in the thermodynamics of topological black holes within massive gravity in higher dimensions.

Findings

Triple points with first-order transitions in $d \\ge 7$

N-fold reentrant phase transitions in $d \\ge 8$

Presence of Van der Waals and reentrant behaviors in various dimensions

Abstract

Massive gravities in anti-de Sitter spacetime can be viewed as effective dual field theories of different phases of condensed matter systems with broken translational symmetry such as solids, (perfect) fluids, and liquid crystals. Motivated by this fact, we explore the black hole chemistry (BHC) of these theories and find a new range of novel phase transitions close to realistic ones in ordinary physical systems. We find that the equation of state of topological black holes (TBHs) at their inflection point(s) in $d$-dimensional spacetime reduces to a polynomial equation of degree $(d-4)$, which yields up to $n=(d-4)$ critical points. As a result, for (neutral) TBHs, we observe triple-point phenomena with the associated first-order phase transitions (in $d \ge 7$), and a new phenomenon we call an $N$-fold reentrant phase transition, in which several ($N$) regions of thermodynamic phase space exhibit distinct reentrant phase transitions, with associated virtual triple points and zeroth-order phase transitions (in $d \ge 8$), as well as Van der Waals transitions (in $d \ge 5$) and reentrant (in $d \ge 6$) behavior. We conclude that BHC in higher-dimensional massive gravity is very likely to offer further new surprises.