Voros product and noncommutative inspired black holes

TL;DR

This paper explores noncommutative inspired black holes using the Voros product, analyzing their entropy, energy relations, and deviations from classical laws, revealing quantum corrections and extremal behavior.

Contribution

It introduces the use of the Voros product in defining noncommutative black holes and derives quantum corrections to entropy and energy relations.

Findings

Area law holds up to exponential corrections

Logarithmic correction to entropy from tunneling formalism

Deviation from standard energy-entropy relation at quantum scale

Abstract

We emphasize the importance of the Voros product in defining noncommutative inspired black holes. The computation of entropy for both the noncommutative inspired Schwarzschild and Reissner-Nordstr\"{o}m black holes show that the area law holds upto order $\frac{1}{\sqrt{\theta}}e^{-M^2/\theta}$. The leading correction to the entropy (computed in the tunneling formalism) is shown to be logarithmic. The Komar energy $E$ for these black holes is then obtained and a deviation from the standard identity $E=2ST_H$ is found at the order $\sqrt{\theta}e^{-M^2/\theta}$. This deviation leads to a nonvanishing Komar energy at the extremal point $T_{H}=0$ of these black holes. The Smarr formula is finally worked out for the noncommutative Schwarzschild black hole. Similar features also exist for a deSitter--Schwarzschild geometry.