Gauss-Bonnet entropy and thermal dynamics of RN-AdS black holes

TL;DR

This paper investigates how the Gauss-Bonnet term modifies the thermodynamics and stability of Reissner-Nordström-AdS black holes, revealing new phase transition behaviors and critical phenomena.

Contribution

It introduces a novel black hole solution with Gauss-Bonnet corrections and analyzes its thermodynamic properties, highlighting the impact of the Gauss-Bonnet term on stability and phase transitions.

Findings

Gauss-Bonnet coupling significantly alters thermodynamic behavior.

Identification of critical points and phase transitions.

Enhanced stability analysis within Gauss-Bonnet gravity.

Abstract

We explore the thermodynamics of a novel solution for the Reissner-Nordstr\"{o}m-Anti-de Sitter (AdS) black hole, uniquely incorporating the Gauss-Bonnet term. Unlike previous studies that primarily focused on standard General Relativity or other modifications, this inclusion allows for a modified entropy formulation, facilitating the computation of key thermodynamic quantities such as Gibbs free energy, the first law of thermodynamics, the equation of state, and Hawking temperature. We identify critical points and graphically represent the relationship between temperature and Gibbs free energy as a function of the horizon radius. Ultimately, we assess the thermal stability of the Reissner-Nordstr\"{o}m-AdS black hole within the framework of Gauss-Bonnet gravity, emphasizing the influence of the Gauss-Bonnet term unlike previous studies that primarily focused on standard General Relativity or other modifications. As a result, it is found that the Gauss-Bonnet coupling significantly alters the thermodynamic behavior and stability structure of the black hole, revealing richer phase transition phenomena.