Phase Transitions in 4D Gauss-Bonnet-de Sitter Black Holes

TL;DR

This paper explores the complex thermodynamic phase structure of four-dimensional Gauss-Bonnet-de Sitter black holes, revealing multiple phase transitions, a triple point, and reentrant phenomena influenced by charge and coupling parameters.

Contribution

It provides the first detailed analysis of phase transitions in 4D Gauss-Bonnet-de Sitter black holes using a Euclidean path integral approach and extended phase space.

Findings

Discovery of Hawking-Page-like and small-large black hole transitions

Identification of a triple point with coexistence of three phases

Observation of reentrant phase transitions between radiation and small black holes

Abstract

We investigate thermodynamic aspects of black holes in the recently formulated four dimensional Gauss-Bonnet theory of gravity, focusing on its asymptotically de Sitter ($\Lambda>0$) solutions. We take a Euclidean path integral approach, where thermodynamic data is fixed at a finite radius `cavity' outside the black hole to achieve equilibrium in the presence of the cosmological horizon. Working in the extended phase space where the cosmological constant is treated as a thermodynamic pressure, we study the phase structure of both uncharged and charged solutions, uncovering a wealth of phenomena. In the uncharged case, black holes are found to undergo either the standard Hawking-Page-like transition to empty de Sitter space or a small-large transition (akin to those seen in charged AdS black holes in pure Einstein gravity) depending on the pressure. We also find a triple point where the radiation, small, and large black hole phases coexist, and a zeroth-order phase transition within a narrow range of Gauss-Bonnet coupling parameter. Reentrant phase transitions between radiation and a small black hole also exist inside a certain parameter range. Similar phenomena are found in the charged case, with the charge parameter playing a role analogous to the Gauss-Bonnet coupling parameter in determining the phase structure.