Black Hole Thermodynamics and Generalized Uncertainty Principle with Higher Order Terms in Momentum Uncertainty

Sunandan Gangopadhyay,Abhijit Dutta

doi:10.1155/2018/7450607

Abstract

We study the modification of thermodynamic properties of Schwarzschild and Reissner-Nordström black hole in the framework of generalized uncertainty principle with correction terms up to fourth order in momentum uncertainty. The mass-temperature relation and the heat capacity for these black holes have been investigated. These have been used to obtain the critical and remnant masses. The entropy expression using this generalized uncertainty principle reveals the area law up to leading order logarithmic corrections and subleading corrections of the form 1/An. The mass output and radiation rate using Stefan-Boltzmann law have been computed which show deviations from the standard case and the case with the simplest form for the generalized uncertainty principle.

Highlights

The consistent unification of quantum mechanics (QM) with general relativity (GR) is one of the major tasks in theoretical physics
It is quite interesting that all approaches towards quantum gravity such as black hole physics [1,2,3], string theory [4, 5], or even Gedanken experiment [6] predict the existence of a minimum measurable length
The occurrence of such a minimal length arises in various theories of quantum gravity phenomenology, namely, the generalized uncertainty principle (GUP) [5, 7, 8], modified dispersion relation (MDR) [9,10,11,12], and deformed special relativity (DSR) [13], to name a few

Summary

Introduction

The consistent unification of quantum mechanics (QM) with general relativity (GR) is one of the major tasks in theoretical physics. It is quite interesting that all approaches towards quantum gravity such as black hole physics [1,2,3], string theory [4, 5], or even Gedanken experiment [6] predict the existence of a minimum measurable length The occurrence of such a minimal length arises in various theories of quantum gravity phenomenology, namely, the generalized uncertainty principle (GUP) [5, 7, 8], modified dispersion relation (MDR) [9,10,11,12], and deformed special relativity (DSR) [13], to name a few. The above studies motivate us to investigate the modification of thermodynamic properties for Schwarzschild and Reissner-Nordstrom (RN) black holes using the form of the GUP proposed in [30] This GUP involves higher order terms in the momentum uncertainty.

Thermodynamics of Schwarzschild Black Hole

Thermodynamics of Reissner-Nordström Black Hole

Conclusions