Thermodynamics and Phase transition of Schwarzschild black hole in Gravity's Rainbow

TL;DR

This paper explores how gravity's rainbow modifies Schwarzschild black hole thermodynamics and phase transitions, revealing new critical behaviors and stability properties distinct from classical Hawking-Page transitions.

Contribution

It introduces two rainbow functions to analyze black hole thermodynamics, providing new insights into phase transitions within gravity's rainbow framework.

Findings

Modified Hawking temperature derived using Heisenberg uncertainty principle

Identification of unique phase transition behaviors different from Hawking-Page transition

Comparison of thermodynamic properties between two rainbow function cases

Abstract

The Planck length and Planck energy should be taken as invariant scales are in agreement with various theories of quantum gravity. In this scenario, the original general relativity can be changed to the so-called gravity's rainbow which produces significant modifications to the black holes' evolution. In this paper, using two kinds of rainbow functions, we investigate the thermodynamics and the phase transition of Schwarzschild black hole in the context of gravity's rainbow theory. Firstly, with the help of the Heisenberg uncertainty principle, we calculate the modified Hawking temperature. Then, based on this modification, we derive the local temperature, free energy and other thermodynamic quantities in an isothermal cavity. Finally, the critical behavior, the thermodynamic stability and phase transition of the rainbow Schwarzschild black hole are analyzed. It turns out that our results are different from the those of Hawking-Page phase transition. Meanwhile, it is found that there are many similarities and differences between rainbow functions I case and rainbow functions II.