Super-entropic black holes in gravity's rainbow and determining constraints on rainbow functions

TL;DR

This study explores the thermodynamic stability of energy-dependent black holes in gravity's rainbow, using the inverse isoperimetric inequality to constrain rainbow functions and demonstrate super-entropic behavior.

Contribution

It introduces a method to constrain rainbow functions in gravity's rainbow by analyzing thermodynamic stability and super-entropic conditions of black holes.

Findings

Black holes satisfy super-entropic condition under certain rainbow function constraints.

Thermodynamic quantities are calculated in extended and non-extended phase spaces.

Constraints on rainbow functions are derived from stability and isoperimetric inequality analysis.

Abstract

This paper is motivated by the application of the inverse isoperimetric inequality to establish constraints on the parameters of gravity's rainbow. We investigate the thermodynamic (in)stability conditions for $d-$dimensional energy-dependent black holes, which are recognized as $d-$ dimensional black holes within the framework of gravity's rainbow. To achieve this, we calculate thermodynamic quantities such as Hawking temperature, entropy, total mass, and heat capacity in both extended and non-extended phase spaces for these black holes. We assess the physical and stable regions by utilizing these thermodynamic quantities alongside the inverse isoperimetric inequality, aiming to determine constraints on the rainbow functions. Finally, we show that by considering a constraint on the rainbow function, these black holes satisfy the super-entropic condition.