Topology of black hole thermodynamics in Gauss-Bonnet gravity

TL;DR

This paper classifies the topological nature of critical points in the thermodynamics of six-dimensional charged Gauss-Bonnet black holes in AdS spacetime, revealing that higher derivative corrections do not alter their topological class and proposing a new interpretation for certain critical points.

Contribution

It applies Duan's $$-mapping theory to classify critical points in Gauss-Bonnet black hole thermodynamics, showing the topological class remains unchanged by higher derivative corrections and introducing a novel phase transition interpretation.

Findings

Higher derivative corrections do not change the topological class of critical points.

The connection between topological nature and phase transitions can break down in certain regimes.

A new interpretation of critical points as phase creation or annihilation points is proposed.

Abstract

Thermodynamics of black holes in anti de Sitter (AdS) spacetimes typically contains critical points in the phase diagram, some of which correspond to the first order transition ending in a second order one. Following the recent proposal in [arXiv:2112.01706] on using Duan's $\phi$-mapping theory, we classify the critical points of six dimensional charged Gauss-Bonnet black holes in AdS spacetime. We find that the higher derivative corrections from Gauss-Bonnet gravity do not change the topological class of critical points in charged black holes in AdS, unlike the case of Born-Infeld corrections noted earlier. The connection between the topological nature of critical points and existence of first order phase transitions breaks down in a certain parameter regime. A resolution is proposed by treating the novel and conventional critical points as phase creation and phase annihilation points, respectively. Examples are provided to support the proposal.