Statistical Entropy of Quantum Black Holes in the Presence of Quantum Gravity Effects

A D Kamali,H Shababi

doi:10.1155/2018/3936169

Abstract

We investigate the effects of deformed algebra, admitted from minimal length, on canonical description of quantum black holes. Using the modified partition function in the presence of all orders of the Planck length, we calculate the thermodynamical properties of quantum black holes. Moreover, after obtaining some thermodynamical quantities including internal energy, entropy, and heat capacity, we conclude that, at high temperature limits due to the decreasing of the number of microstates, the entropy tends to upper bounds.

Highlights

As it is known, one of the most important results of introducing General Relativity (GR) is the development of human’s insight of the universe
GR seems to be a purely classical theory, for some major applications such as cosmology and black hole (BH) theories, the quantization of gravity is the main problem of theoretical physics community
It is worth mentioning that all approaches to QG scenario including string theory, noncommutative geometry, and loop quantum gravity (LQG) have shown the existence of a minimal measurable length [2, 3]

Summary

Introduction

One of the most important results of introducing General Relativity (GR) is the development of human’s insight of the universe. One way to survey some phenomenological aspects of effective QG candidates is the deformation of algebraic structure of ordinary quantum mechanics In this sense, the generalized uncertainty principle [4, 5] and noncommutative geometry [6, 7] can be mentioned as the most famous deformations which impose the ultraviolet and infrared cutoffs for the physical systems [8, 9]. It is shown that our results coincide with those obtained from full quantum considerations in the limit of high temperature Since this way is appropriate to investigate the thermodynamical properties of quantum black holes, we use that to study thermodynamics of the quantum black hole in new framework and find corrections to the Hawking entropy. It should be noted that our method can be very interesting because we obtain solutions without solving the Hamiltonian eigenvalue problem

Quantum Corrections to Black Holes

The Effects of Deformed Algebra on Some Thermodynamical Quantities

Deformed Algebra on the Quantum Black Hole

Summary and Conclusions