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

TL;DR

The paper studies charged SAdS and SdS black holes in five-dimensional Einstein-Gauss-Bonnet gravity with Maxwell fields, focusing on thermodynamics and phase structure. It develops both the bulk solutions and the holographic boundary counterterms needed to define conserved masses and entropies, and reveals a GB/charge-driven phase diagram with a critical line for Hawking-Page transitions. A central finding is that higher-derivative corrections can yield negative or zero entropy for certain parameter ranges, suggesting possible instabilities and a novel SdS↔SAdS transmutation mechanism via zero-entropy states. The work also discusses dS/CFT localization of gravity and provides a framework for black hole thermodynamics in higher-derivative gravity with implications for holography and brane cosmology.

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.

Figures (2)

• Figure 1: The phase diagrams when $\epsilon<{1 \over 2}$
• Figure 2: The phase diagrams when $\epsilon>{1 \over 2}$