# Thermodynamics of Rotating Kaluza-Klein Black Holes in Gravity's Rainbow

## TL;DR

This paper investigates how rainbow functions inspired by quantum gravity modify the thermodynamics of rotating Kaluza-Klein black holes, revealing the existence of Planck-scale remnants and similar critical phenomena.

## Contribution

It introduces a novel deformation of rotating Kaluza-Klein black holes using rainbow functions from loop quantum gravity and non-commutative geometry, analyzing their thermodynamic behavior.

## Key findings

- Deformed temperature and entropy indicate Planckian remnants.
- Both ordinary and deformed black holes exhibit similar critical behavior.
- Thermodynamic properties are significantly altered by rainbow functions.

## Abstract

In this paper, a four dimensional rotating Kaluza Klien (K-K) black hole was deformed using rainbow functions derived from loop quantum gravity and non-commutative geometry. We studied the thermodynamic properties and critical phenomena of this deformed black hole. The deformed temperature and entropy showed the existence of a Planckian remnant. The calculation of Gibbs free energy $ G$ for the ordinary and deformed black holes showed that both share a similar critical behaviour.