Comment on "Thermodynamic properties of Schwarzschild black hole in non-commutative gauge theory of gravity"

TL;DR

This paper critically reviews a recent study on the thermodynamics of a non-commutative black hole, highlighting computational errors and invalid conclusions, and emphasizes the need for a proper reanalysis.

Contribution

It provides a detailed critique of previous work, identifying specific errors in calculations and assumptions that invalidate earlier thermodynamic results.

Findings

Incorrect event horizon calculation identified

Misapplication of surface gravity definition

Previous thermodynamic conclusions are invalid

Abstract

A recent study [Annals Phys. 455 (2023) 169394, e-Print: 2204.01901 [gr-qc]] examined the thermodynamic behavior of an axially symmetric black hole within a non-commutative framework that mimics the effect of an angular momentum. However, the analysis presents notable computational inconsistencies. In that analysis, the event horizon was miscalculated, and this error propagated through and compromised all subsequent results. In addition, an incorrect definition of surface gravity was used -- the spherically symmetric case was invoked for an axially symmetric spacetime -- rendering the thermodynamic results invalid. In other words, all the results presented in the paper require a thorough reexamination.