Thermodynamics of static and stationary black holes in Einstein-Gauss-Bonnet gravity with dark matter

Abstract: This paper studies Einstein-Gauss-Bonnet (EGB) black holes surrounded by three phenomenological distributions of dark matter halos. The main result is obtaining the analytical solutions for the metric and all thermodynamic quantities, such as Hawking temperature, entropy, constant-volume heat capacity, and Gibbs free energy for static and stationary black hole solutions. Consequently, we determine a non-null horizon radius at which the black hole halts its evaporation by vanishing the temperature, indicating the emergence of remnants. In the stationary case, we also obtain the ergosphere regions for the found solutions and compare them. Finally, we find local and global phase transitions by studying the behavior of the heat capacity and Gibbs free energy.