On the thermodynamic phase structure of conformal gravity

TL;DR

This paper investigates the complex thermodynamic phase structure of four-dimensional conformal gravity in AdS space, revealing unique phenomena such as multiple phase branches, negative volume, and phase transitions, influenced by a key metric parameter.

Contribution

It provides a detailed analysis of the thermodynamic phase behavior of conformal gravity, highlighting features distinct from Einstein gravity, especially the effects of the parameter c_1.

Findings

Presence of two branches of equations of state

Existence of negative thermodynamic volume

Identification of zeroth-order and Hawking-Page-like phase transitions

Abstract

The solutions of the Einstein equation are a subset of the solutions of conformal (Weyl) gravity, but the difference from the action means that the black hole thermodynamics of the two gravity theories would be different. In this paper we explore the thermodynamic phase structure for the conformal gravity in the four-dimensional AdS space-time. Special emphasis is put on the dependence on the parameter $c_1$ in the linear-$r$ term in the metric. The thermodynamic phase structure of the conformal gravity is very rich, including two branches of equations of states, negative thermodynamic volume, zeroth-order phase transition, and Hawking-Page like phase transition.