Bound of Noncommutativity Parameter Based on Black Hole Entropy

TL;DR

This paper derives a lower bound on the noncommutativity parameter in a noncommutative Schwarzschild black hole by analyzing entropy and cutoff relations, linking quantum gravity effects to black hole thermodynamics.

Contribution

It establishes a quantitative lower bound on the noncommutativity parameter using black hole entropy and the brick wall method, connecting noncommutative geometry with black hole physics.

Findings

Noncommutativity parameter bounded as $ heta > 8.4 imes 10^{-2} l_p$

Entropy satisfies the area law in the noncommutative black hole

Cutoff relation depends on the noncommutativity parameter

Abstract

We study the bound of the noncommutativity parameter in the noncommutative Schwarzschild black hole which is a solution of the noncommutative ISO(3,1) Poincare gauge group. The statistical entropy satisfying the area law in the brick wall method yields a cutoff relation which depends on the noncommutativity parameter. Requiring both the cutoff parameter and the noncommutativity parameter to be real, the noncommutativity parameter can be shown to be bounded as $\Theta > 8.4\ times 10^{-2}l_{p}$.