Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole

G Abbas

doi:10.1155/2014/306256

Abstract

Few years ago, Setare (2006) has investigated the Cardy-Verlinde formula of noncommutative black hole obtained by noncommutativity of coordinates. In this paper, we apply the same procedure to a noncommutative black hole obtained by the coordinate coherent approach. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal field theory to its total energy and Casimir energy. In this paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of noncommutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula.

Highlights

Verlinde [1] proved that the entropy of conformal field theory in arbitrary dimension is related to its total energy and Casimir energy; this is known as generalized Verlinde formula
The purpose of this paper is to investigate the validity of Cardy-Verlinde entropy formula for NC Schwarzschild black hole (BH)
Motivated by the recent development in NC theory of gravity, we have proved that the entropy of NC Schwarzschild BH horizon can be expressed in terms of Cardy-Verlinde formula

Summary

Introduction

Verlinde [1] proved that the entropy of conformal field theory in arbitrary dimension is related to its total energy and Casimir energy; this is known as generalized Verlinde formula (commonly termed as Cardy-Verlinde formula). In classical general relativity (GR), the curvature singularity is such a point where physical description of the gravitational field is impossible This problem can be removed in GR by taking into account the quantum mechanical treatment to the standard formulation of GR. Motivated by the recent development in NC theory of gravity, we have proved that the entropy of NC Schwarzschild BH horizon can be expressed in terms of Cardy-Verlinde formula. For this purpose, we have used the Setare and Jamil method [5].

Noncommutative Schwarzschild Black Hole and Cardy-Verlinde Formula

Outlook