Thermodynamics, phase structure of Bardeen massive black hole in Gauss-Bonnet gravity

Abstract

This work provides the exact solution of the Bardeen black hole in association with [Formula: see text] Gauss–Bonnet massive gravity in Anti-de-Sitter [Formula: see text] space–time. It is a modification of the Gauss–Bonnet when gravity couples with nonlinear matter fields which is the function of the electromagnetic field. The obtained solution gives rise to [Formula: see text] EGB Bardeen black holes when the massive gravity parameter is set to zero and it yields a [Formula: see text] Gauss–Bonnet black hole in the absence of magnetic monopole charge. Further, we analyze and adopt the thermodynamic quantities like mass ([Formula: see text]), temperature [Formula: see text] and heat capacity [Formula: see text] in the presence of massive gravity and nonlinear electrodynamics. In addition, we extend our results by considering the cosmological constant [Formula: see text] as a thermodynamical variable [Formula: see text] and obtain the critical values of pressure, temperature, horizon radius and analyze the behavior of the global parameter [Formula: see text]. The effect of a massive parameter ([Formula: see text]) of the critical exponent is opposite to the magnetic monopole charge ([Formula: see text]) and Gauss–Bonnet parameter ([Formula: see text]). According to our analysis the phase transition between a small and large black hole and van der Waals phase transition are analogous to each other.