Black Holes in Gauss-Bonnet Gravity's Rainbow

TL;DR

This paper introduces a generalized energy-dependent Gauss-Bonnet gravity theory coupled with Maxwell's theory, analyzing black hole solutions and their thermodynamics, revealing modifications but preserving the first law of thermodynamics.

Contribution

It extends Gauss-Bonnet gravity to an energy-dependent framework called gravity's rainbow and studies black hole solutions within this new context.

Findings

Black hole solutions are obtained in the energy-dependent Gauss-Bonnet gravity.

Thermodynamics of black holes is modified but the first law remains valid.

Thermal stability of black holes is analyzed within this framework.

Abstract

In this paper, we will generalize the Gauss-Bonnet gravity to an energy dependent Gauss-Bonnet theory of gravity, which we shall call as the Gauss-Bonnet gravity's rainbow. We will also couple this theory to a Maxwell's theory. We will analyze black hole solutions in this energy dependent Gauss-Bonnet gravity's rainbow. We will calculate the modifications to the thermodynamics of black holes in the Gauss-Bonnet's gravity's rainbow. We will demonstrate that even though the thermodynamics of the black holes get modified in the Gauss-Bonnet gravity's rainbow, the first law of thermodynamics still holds for this modified thermodynamics. We will also comment on the thermal stability of the black hole solutions in this theory.