Black holes surrounded by modified Chaplygin gas in Lovelock theory of gravity

Abstract

The Lovelock theory of gravity is a natural extension of the Einstein’s theory of general relativity to higher dimensions, which presents the criteria of general covariance and is free of ghosts. In this work, we consider a model that static spherically-symmetric black hole is surrounded by the modified Chaplygin gas with equation of state p=Aρ−B/ρα. We find that the energy density of the modified Chaplygin gas can be characterized by four parameters. The black hole thermodynamical quantities, consisting of gravitational mass, temperature, entropy and heat capacity, as functions of horizon radius, are calculated. Concerning the thermodynamical stability of the black holes, we consider the third-order Lovelock gravity as a specific case and show in figures the heat capacity versus the horizon radius, observing that there exist a phase of thermodynamically stable small black hole and a phase of thermodynamically unstable large black hole for D=7, while an additional intermediate local unstable phase as well as an intermediate local stable phase appear for D=8 with configuring properly the model parameters. The effects of the modified Chaplygin gas and Lovelock gravity on thermodynamical stability of the black holes are discussed.