Abstract
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.
Highlights
James Clark Maxwell is one of the physicists who played the most decisive part in developing the electrodynamics
The main goal of this paper is to find topological black hole solutions of the Gauss–Bonnet Born–Infeld (GB–BI) gravity with an energy dependent spacetime
It is worth mentioning that all higher curvature gravity, higher dimensional physics, higher curvature terms in gauge theory, and the existence of upper limit for the energy of a particle can be originated from heterotic string theory and modified dispersion relation, which are two fundamental acceptable theories
Summary
James Clark Maxwell is one of the physicists who played the most decisive part in developing the electrodynamics. Among generalizations of the Einstein–Maxwell action to a higher curvature gauge–gravity theory, the GB–BI gravity has some particular interests because it is a ghost-free theory in the gravitational side and a divergence-free field in the electromagnetic side Both GB and BI theories emerge in the effective low-energy action of string theory [3,4,5,6,7,8,9,10,11,12,13,14]. It is worth mentioning that all higher curvature gravity, higher dimensional physics, higher curvature terms in gauge theory, and the existence of upper limit for the energy of a particle can be originated from heterotic string theory and modified dispersion relation, which are two fundamental acceptable theories. We study thermal stability and analyze the effects of GB, BI, rotation parameters and rainbow functions on stability criteria
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