Noncommutative inspired Schwarzschild black hole, Voros product and Komar energy

TL;DR

This paper explores noncommutative Schwarzschild black holes using the Voros product, revealing entropy corrections, a deformation of the energy-temperature relation, and implications for the black hole's thermodynamics.

Contribution

It introduces the use of the Voros product in noncommutative black hole models and analyzes resulting entropy and energy relations, including corrections and deformations.

Findings

Entropy obeys the area law up to exponential corrections.

Logarithmic correction to the entropy is identified.

Deformation of the Komar energy relation is found at noncommutative scales.

Abstract

The importance of the Voros product in defining a noncommutative Schwarzschild black hole is shown. The entropy is then computed and the area law is shown to hold 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 deformation from the conventional identity $E=2ST_H$ is found at the order $\sqrt{\theta}e^{-M^2/\theta}$. This deformation leads to a nonvanishing Komar energy at the extremal point $T_{H}=0$ of these black holes. Finally, the Smarr formula is worked out. Similar features also exist for a deSitter-Schwarzschild geometry. This presentation is based on the work in references [1,2].