Black hole solution and thermal properties in 4DAdS Gauss-Bonnet massive gravity

We consider an Einstein-Gauss-Bonnet massive gravity model in 4DAdS 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.

Automated summary

This study investigates an Einstein-Gauss-Bonnet massive gravity model in 4DAdS spacetime to obtain a black hole solution and analyze its horizon structure. Various types of horizons are found based on the real roots of the metric function. Thermodynamic quantities are derived, confirming the validity of the first law of thermodynamics and the Smarr relation. The presence of the massive gravity parameter affects the thermodynamic quantities and the system's stability is discussed based on heat capacity. When treating the cosmological constant as the thermodynamic pressure, black hole spacetimes exhibit not only standard thermodynamics but also phase structures. The influence of the massive parameter and GB parameter on phase transition is also examined.