Thermodynamic phase transition in the rainbow Schwarzschild black hole

TL;DR

This paper investigates the thermodynamic phase transitions of rainbow Schwarzschild black holes, revealing an additional critical temperature and explaining the finiteness of temperature near the horizon through a running gravitational coupling.

Contribution

It introduces a modified thermodynamic framework for rainbow black holes, identifying new critical phenomena and explaining horizon temperature finiteness via quantum gravity effects.

Findings

Discovery of an additional critical temperature for black hole stability.

Identification of a locally stable tiny black hole state.

Explanation of finite temperature near the horizon using running gravitational coupling.

Abstract

We study the thermodynamic phase transition in the rainbow Schwarzschild black hole where the metric depends on the energy of the test particle. Identifying the black hole temperature with the energy from the modified dispersion relation, we obtain the modified entropy and thermodynamic energy along with the modified local temperature in the cavity to provide well defined black hole states. It is found that apart from the conventional critical temperature related to Hawking-Page phase transition there appears an additional critical temperature which is of relevance to the existence of a locally stable tiny black hole; however, the off-shell free energy tells us that this black hole should eventually tunnel into the stable large black hole. Finally, we discuss the reason why the temperature near the horizon is finite in the rainbow black hole by employing the running gravitational coupling constant, whereas it is divergent near the horizon in the ordinary Schwarzschild black hole.