# Thermodynamics of BTZ Black Holes in Gravity's Rainbow

## TL;DR

This paper investigates how gravity's rainbow modifies the thermodynamics of BTZ black holes, revealing the existence of remnants and specific invariances in Gibbs free energy due to the deformation effects.

## Contribution

It introduces a deformation of BTZ black hole thermodynamics based on rainbow functions from loop quantum gravity and noncommutative geometry, highlighting unique invariance properties.

## Key findings

- Thermodynamics is deformed by rainbow functions, indicating black hole remnants.
- Gibbs free energy remains unaffected by rainbow deformations.
- Entropy and temperature deformations cancel out in Gibbs free energy calculation.

## Abstract

In this paper, we deform the thermodynamics of a BTZ black hole from rainbow functions in gravity's rainbow. The rainbow functions will be motivated from results in loop quantum gravity and Noncommutative geometry. It will be observed that the thermodynamics gets deformed due to these rainbow functions, indicating the existence of a remnant. However, the Gibbs free energy does not get deformed due to these rainbow functions, and so the critical behaviour from Gibbs does not change by this deformation.This is because the deformation in the entropy cancel's out the temperature deformation.