Critical behavior of charged black holes in Gauss-Bonnet gravity`s rainbow

TL;DR

This paper explores the thermodynamics and critical phenomena of charged Gauss-Bonnet black holes within gravity's rainbow framework, revealing energy-dependent effects and van der Waals-like phase transitions.

Contribution

It introduces an energy-dependent generalization of Gauss-Bonnet black holes and analyzes their thermodynamics and phase behavior, including critical points and restrictions due to charge.

Findings

Identification of van der Waals-like phase transitions in rainbow black holes.

Energy dependence affects thermodynamical properties and critical behavior.

Charged solutions impose parameter restrictions based on energy dependence.

Abstract

Following an earlier study regarding Gauss-Bonnet-Maxwell black holes in the presence of gravity's rainbow [S. H. Hendi and M. Faizal, Phys. Rev. D 92, 044027 (2015)], in this paper, we will consider all constants as energy dependent ones. The geometrical and thermodynamical properties of this generalization are studied and the validation of the first law of thermodynamics is examined. Next, through the use of proportionality between cosmological constant and thermodynamical pressure, van der Waals-like behavior of these black holes in extended phase space is investigated. An interesting critical behavior for sets of rainbow functions in this case is reported. Also, the critical behavior of uncharged and charged solutions is analyzed and it is shown that the generalization to a charged case puts an energy dependent restriction on values of different parameters.