Restricted phase space thermodynamics for black holes in higher dimensions and higher curvature gravities

TL;DR

This paper extends restricted phase space thermodynamics to higher-dimensional, higher-curvature black hole models, revealing different thermodynamic behaviors and phase transition properties among Einstein-Hilbert, Born-Infeld, and Chern-Simons gravity models.

Contribution

It demonstrates the applicability of restricted phase space thermodynamics to a broad class of higher curvature gravity models and compares their thermodynamic phase structures.

Findings

Einstein-Hilbert and Born-Infeld models show similar phase transition behaviors.

Chern-Simons model exhibits distinct thermodynamic properties.

Universal behavior observed in some models, while others differ significantly.

Abstract

The recently proposed restricted phase space thermodynamics is shown to be applicable to a large class of higher dimensional higher curvature gravity models coupled to Maxwell field, which are known as black hole scan models and are labeled by the spacetime dimension $d$ and the highest order $k$ of the Lanczos-Lovelock densities appearing in the action. Three typical example cases with $(d,k)=(5,1), (5,2)$ and $(6,2)$ are chosen as example cases and studied in some detail. These cases are representatives of Einstein-Hilbert, Chern-Simons and Born-Infield like gravity models. Our study indicates that the Einstein-Hilbert and Born-Infield like gravity models have similar thermodynamic behaviors, e.g. the existence of isocharge $T-S$ phase transitions with the same critical exponents, the existence of isovoltage $T-S$ transitions and the Hawking-Page like transitions, and the similar high temperature asymptotic behaviors for the isocharge heat capacities, etc. However, the Chern-Simons like $(5,2)$-model behaves quite differently. Neither isocharge nor isovoltage $T-S$ transitions could occur and no Hawking-Page like transition is allowed. This seems to indicate that the Einstein-Hilbert and Born-Infield like models belong to the same universality class while the Chern-Simons like models do not.