Thermodynamics of Gauss-Bonnet black holes revisited

TL;DR

This paper explores the thermodynamics of five-dimensional Gauss-Bonnet anti-de Sitter black holes, revealing how the Gauss-Bonnet coupling influences their properties and stability, and proposing a link between stability and quasinormal modes.

Contribution

It provides a comprehensive thermodynamic analysis of GBAdS black holes, highlighting the role of the coupling constant and establishing differences from standard AdS black holes.

Findings

For negative coupling, thermodynamic quantities are not positive definite.

Positive coupling yields BIAdS-like black holes with pseudo-charge behavior.

GBAdS black holes differ fundamentally from Schwarzschild-AdS in the zero-coupling limit.

Abstract

We investigate the Gauss-Bonnet black hole in five dimensional anti-de Sitter spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which is characterized by the Gauss-Bonnet coupling $c$ and mass $M$, comparing with those of the Born-Infeld-AdS (BIAdS), Reissner-Norstr\"om-AdS black holes (RNAdS), Schwarzschild-AdS (SAdS), and BTZ black holes. For $c<0$ we cannot obtain the black hole with positively definite thermodynamic quantities of mass, temperature, and entropy because the entropy does not satisfy the area-law. On the other hand, for $c>0$, we find the BIAdS-like black hole, showing that the coupling $c$ plays the role of pseudo-charge. Importantly, we could not obtain the SAdS in the limits of $c\to 0$, which means that the GBAdS is basically different from the SAdS. In addition, we clarify the connections between thermodynamic and dynamical stability. Finally, we also conjecture that if a black hole is big and thus globally stable, its quasinormal modes may take analytic expressions.