Thermodynamic phase transition of a black hole in rainbow gravity

TL;DR

This paper studies how rainbow gravity modifies the thermodynamics and phase transitions of Schwarzschild black holes, revealing new critical behaviors and black hole remnants due to quantum gravity effects.

Contribution

It introduces a detailed analysis of thermodynamic properties and phase transitions of rainbow Schwarzschild black holes, highlighting the impact of rainbow gravity on black hole evolution.

Findings

Rainbow gravity halts Hawking radiation, creating black hole remnants.

Identifies one first-order and multiple second-order phase transitions.

Discovers several Hawking-Page-type phase transitions in rainbow gravity.

Abstract

In this letter, using the rainbow functions that were proposed by Magueijo and Smolin, we investigate the thermodynamics and the phase transition of rainbow Schwarzschild black hole. First, we calculate the rainbow gravity corrected Hawking temperature. From this modification, we then derive the local temperature, free energy, and other thermodynamic quantities in an isothermal cavity. Finally, we analyze the critical behavior, thermodynamic stability, and phase transition of the rainbow Schwarzschild black hole. The results show that the rainbow gravity can stop the Hawking radiation in the final stages of black holes' evolution and lead to the remnants of black holes. Furthermore, one can observe that the rainbow Schwarzschild black hole has one first-order phase transition, two second-order phase transitions, and three Hawking-Page-type phase transitions in the framework of rainbow gravity theory.