Energy-dependent topological anti-de Sitter black holes in Gauss-Bonnet Born-Infeld gravity

Employing higher curvature corrections to Einstein--Maxwell gravity has garnered a great deal of attention motivated by the high energy regime in quantum nature of black hole physics. In addition, one may employ gravity's rainbow to encode quantum gravity effects into the black hole solutions. In this paper, we regard an energy dependent static spacetime with various topologies and study its black hole solutions in the context of Gauss--Bonnet Born--Infeld (GB--BI) gravity. We study thermodynamic properties and examine the first law of thermodynamics. Using suitable local transformation, we endow the Ricci--flat black hole solutions with a global rotation and study the effects of rotation on thermodynamic quantities. We also investigate thermal stability in canonical ensemble through calculating the heat capacity. We obtain the effects of various parameters on the horizon radius of stable black holes. Finally, we discuss second order phase transition in the extended phase space thermodynamics and investigate the critical behavior.