Maximally Localized States and Quantum Corrections of Black Hole Thermodynamics in the Framework of a New Generalized Uncertainty Principle

Yan-Gang Miao,Ying-Jie Zhao,Shao-Jun Zhang

doi:10.1155/2015/627264

Abstract

As a generalized uncertainty principle (GUP) leads to the effects of the minimal length of the order of the Planck scale and UV/IR mixing, some significant physical concepts and quantities are modified or corrected correspondingly. On the one hand, we derive the maximally localized states—the physical states displaying the minimal length uncertainty associated with a new GUP proposed in our previous work. On the other hand, in the framework of this new GUP we calculate quantum corrections to the thermodynamic quantities of the Schwardzschild black hole, such as the Hawking temperature, the entropy, and the heat capacity, and give a remnant mass of the black hole at the end of the evaporation process. Moreover, we compare our results with that obtained in the frameworks of several other GUPs. In particular, we observe a significant difference between the situations with and without the consideration of the UV/IR mixing effect in the quantum corrections to the evaporation rate and the decay time. That is, the decay time can greatly be prolonged in the former case, which implies that the quantum correction from the UV/IR mixing effect may give rise to a radical rather than a tiny influence to the Hawking radiation.

Highlights

To unify general relativity and quantum mechanics is one of the most difficult tasks because the existing quantum gravity theories are ultraviolet divergent and nonrenormalizable
In the framework of the exponential generalized uncertainty principle (GUP), the quantum corrections to the thermodynamic quantities of the Schwardzschild black hole are computed and some interesting results related to the black hole evaporation process are obtained, such as the faster evaporation and larger remnant mass than that deduced in the framework of the quadratic GUP
We turn to the Hawking evaporation process of the Schwarzschild black hole and calculate the quantum corrections to the evaporation rate and the decay time in Section 4, where we focus on the significant difference between the situations without and with the consideration of the UV/IR mixing effect

Summary

Introduction

To unify general relativity and quantum mechanics is one of the most difficult tasks because the existing quantum gravity theories are ultraviolet divergent and nonrenormalizable. Based on the quadratic GUP, the maximally localized states are derived [10] and developed [16] for a class of quite general GUPs. In the framework of the exponential GUP, the quantum corrections to the thermodynamic quantities of the Schwardzschild black hole are computed and some interesting results related to the black hole evaporation process are obtained, such as the faster evaporation and larger remnant mass than that deduced in the framework of the quadratic GUP. In the present paper we revisit the maximally localized states and the quantum corrections to the thermodynamic quantities of the Schwardzschild black hole in the framework of our newly proposed GUP [38], the so-called improved exponential GUP (noted by GUPn for the same purpose as GUP0 and GUP1).

The Improved Exponential GUP and Its Corresponding Maximally Localized States

Black Hole Thermodynamics

Black Hole Evaporation

Conclusion