The thermodynamics and phase transition of a rainbow black hole

TL;DR

This paper introduces new rainbow functions incorporating the generalized uncertainty principle to study thermodynamics and phase transitions of rainbow Schwarzschild black holes, revealing effects like black hole remnants and multiple phase transitions.

Contribution

It develops a novel rainbow function model with GUP parameter and analyzes its impact on black hole thermodynamics and phase transitions, extending previous studies.

Findings

Rainbow gravity and GUP prevent total black hole evaporation.

Multiple phase transitions occur in the thermodynamic system.

Black hole remnants are formed due to modified Hawking radiation.

Abstract

In this work, we construct a new kind of rainbow functions, which has generalized uncertainty principle parameter. Then, we investigate modified thermodynamic quantities and phase transition of rainbow Schwarzschild black hole by employing this new kind of rainbow functions. Our results demonstrate that the rainbow gravity and generalized uncertainty principle have a great effect on the picture of Hawking radiation. They prevent black holes from total evaporation and cause a remnant. In addition, after analyzing the modified local thermodynamic quantities, we find that the effect of rainbow gravity and the generalized uncertainty principle lead to one first-order phase transition, two second-order phase transitions, and two Hawking-Page-type phase transitions in the thermodynamic system of rainbow Schwarzschild black hole.