Charged Black Hole Solutions in Gauss-Bonnet-Massive Gravity

TL;DR

This paper explores charged black hole solutions within Gauss-Bonnet-massive gravity, analyzing their thermodynamics, stability, phase transitions, and critical behavior using various thermodynamic methods and extended phase space analysis.

Contribution

It introduces a comprehensive study of black holes in Gauss-Bonnet-massive gravity, including thermodynamics, stability, phase transitions, and a novel method for critical point determination.

Findings

Black hole horizon types depend on parameters.

Thermodynamic quantities satisfy the first law.

Phase transition points are parameter-dependent.

Abstract

Motivated by high interest in the close relation between string theory and black hole solutions, in this paper, we take into account the Einstein-Gauss-Bonnet Lagrangian in the context of massive gravity. We examine the possibility of black hole in this regard, and discuss the types of horizons. Next, we calculate conserved and thermodynamic quantities and check the validity of the first law of thermodynamics. In addition, we investigate the stability of these black holes in context of canonical ensemble. We show that number, type and place of phase transition points may be significantly affected by different parameters. Next, by considering cosmological constant as thermodynamical pressure, we will extend phase space and calculate critical values. Then, we construct thermodynamical spacetime by considering mass as thermodynamical potential. We study geometrical thermodynamics of these black holes in context of heat capacity and extended phase space. We show that studying heat capacity, geometrical thermodynamics and critical behavior in extended phase space lead to consistent results. Finally, we will employ a new method for obtaining critical values and show that the results of this method are consistent with those of other methods.