Noncommutative Schwarzschild Black Hole and Area Law

TL;DR

This paper investigates the validity of the Bekenstein-Hawking area law for noncommutative Schwarzschild black holes, showing it holds for larger horizons and detailing corrections for smaller horizons.

Contribution

It provides a graphical analysis confirming the area law for certain horizon sizes and derives corrections for smaller horizons in noncommutative black holes.

Findings

Area law holds for horizon radius greater than approximately 4.8√θ.

Corrections to the area law are derived for smaller horizons.

Exact entropy behavior is characterized down to the extremal point at 3.0√θ.

Abstract

Using a graphical analysis, we show that for the horizon radius $r_h\gtrsim 4.8\sqrt\theta$, the standard semiclassical Bekenstein-Hawking area law for noncommutative Schwarzschild black hole exactly holds for all orders of $\theta$. We also give the corrections to the area law to get the exact nature of the Bekenstein-Hawking entropy when $r_h<4.8\sqrt\theta$ till the extremal point $r_h=3.0\sqrt{\theta}$.