On the Komar Energy and the Generalized Smarr Formula for a Charged Black Hole of Noncommutative Geometry

TL;DR

This paper calculates the Komar energy for a noncommutative charged black hole and derives a deformed Smarr formula, revealing how noncommutative geometry modifies classical black hole thermodynamics.

Contribution

It introduces a generalized Smarr formula for noncommutative charged black holes, highlighting the impact of noncommutative geometry on black hole energy relations.

Findings

Derived the Komar energy for noncommutative charged black holes.

Established a generalized Smarr formula incorporating noncommutative effects.

Showed the deformation from classical relations depends on the noncommutative scale length.

Abstract

We calculate the Komar energy $E$ for a charged black hole inspired by noncommutative geometry and identify the total mass ($M_{0}$) by considering the asymptotic limit. We also found the generalized Smarr formula, which shows a deformation from the well known relation $M_{0}-\frac{Q_{0}^{2}}{r}=2ST$ depending on the noncommutative scale length $\ell$ .