Constraints on rainbow gravity functions from black hole thermodynamics

TL;DR

This paper explores how rainbow gravity modifies black hole thermodynamics, constraining the possible rainbow functions by requiring universal entropy corrections, and compares the results to those from the generalized uncertainty principle.

Contribution

It introduces constraints on rainbow gravity functions based on black hole entropy corrections and analyzes their effects on black hole thermodynamics.

Findings

Existence of remnant and critical masses in rainbow gravity

Constraints on rainbow functions from entropy correction universality

Similarity between rainbow gravity and generalized uncertainty principle results

Abstract

In this paper, we investigate the thermodynamic properties of black holes in the framework of rainbow gravity. By considering rainbow functions in the metric of Schwarzschild and Reissner-Nordstr\"{o}m black holes, remnant and critical masses are found to exist. Demanding the universality of logarithmic corrections to the semi-classical area law for the entropy leads to constraining the form of the rainbow functions. The mass output and the radiation rate for these constrained form of rainbow functions have been computed for different values of the rainbow parameter $\eta$ and have striking similarity to those derived from the generalized uncertainty principle.