Black hole solution and thermal properties in $4D$ AdS Gauss-Bonnet massive gravity

TL;DR

This paper explores a novel 4D AdS black hole solution within Einstein-Gauss-Bonnet massive gravity, analyzing its horizon structure, thermodynamics, stability, and phase transitions influenced by massive and Gauss-Bonnet parameters.

Contribution

It introduces a new 4D AdS black hole solution in Einstein-Gauss-Bonnet massive gravity and studies its thermodynamic behavior and phase transitions.

Findings

Black hole horizons depend on the metric function roots.

Thermodynamics obeys the first law and Smarr relation.

Phase transitions occur at specific pressures, with first and second order transitions identified.

Abstract

We consider an Einstein-Gauss-Bonnet massive gravity model in $4D$ AdS spacetime to obtain a possible black hole solution and discuss the horizon structure of this black hole. The real roots of the vanishing metric function lead to various types of horizons. Furthermore, we derive various thermodynamic quantities, thus insuring the validity of the first-law of thermodynamics and the Smarr relation. The thermodynamic quantities are modified in the presence of the massive gravity parameter and also discuss the stability of the system from the heat capacity. Black hole space times can not only possess standard thermodynamics, but also possess phase structures when the cosmological constant is treated as the thermodynamic pressure. The effects of massive parameter and GB parameter on phase transition are also discussed. We also examine the phase structure through Maxwell's equal area law. The first order phase transition occurs only when pressure is lower than its critical value. At critical pressure, the first order phase transition terminates, and the second order phase transition occurs. No phase transition occurs when pressure is greater than its critical value.