Black Hole Thermodynamics and Negative Entropy in deSitter and Anti-deSitter Einstein-Gauss-Bonnet gravity

TL;DR

This paper explores the thermodynamics of black holes in 5d Einstein-Gauss-Bonnet gravity, revealing the possibility of negative entropy states and their implications for stability and phase transitions in de Sitter and Anti-de Sitter spaces.

Contribution

It introduces the analysis of black hole thermodynamics with higher derivative terms, including negative entropy scenarios, within the framework of Einstein-Gauss-Bonnet gravity and dS/CFT correspondence.

Findings

Phase diagrams for charged SAdS black holes are constructed.

Negative entropy states are possible depending on higher derivative parameters.

A potential instability transition between negative and positive entropy black holes is proposed.

Abstract

We investigate the charged Schwarzschild-Anti-deSitter (SAdS) BH thermodynamics in 5d Einstein-Gauss-Bonnet gravity with electromagnetic field. The Hawking-Page phase transitions between SAdS BH and pure AdS space are studied. The corresponding phase diagrams (with critical line defined by GB term coefficient and electric charge) are drawn. The possibility to account for higher derivative Maxwell terms is mentioned. In frames of proposed dS/CFT correspondence it is demonstrated that brane gravity maybe localized similarly to AdS/CFT. SdS BH thermodynamics in 5d Einstein and Einstein-Gauss-Bonnet gravity is considered. The corresponding (complicated) surface counterterms are found and used to get the conserved BH mass, free energy and entropy. The interesting feature of of higher derivative gravity is the possibility for negative (or zero) SdS (or SAdS) BH entropy which depends on the parameters of higher derivative terms. We speculate that the appearence of negative entropy may indicate a new type instability where a transition between SdS (SAdS) BH with negative entropy to SAdS (SdS) BH with positive entropy would occur.