On the consistency of non-commutative geometry inspired Reissner-Nordstr\"{o}m black hole solution

TL;DR

This paper examines the non-commutative geometry inspired Reissner-Nordström black hole, revealing inconsistencies in Einstein equations and proposing an improved energy-momentum tensor that alters the predicted violation of energy conditions.

Contribution

It introduces a consistent energy-momentum tensor for the non-commutative black hole, correcting previous inconsistencies and affecting the understanding of energy condition violations.

Findings

Not all Einstein equations are satisfied by the original solution.

The improved tensor leads to different predictions for energy condition violations.

Violations may occur outside the Cauchy horizon, impacting observational prospects.

Abstract

We revisit the non-commutative geometry inspired Reissner-Nordstr\"{o}m black hole solution obtained by smearing the point sources with a Gaussian distribution. We show that while the form of the metric function and the physical properties derived from that remain valid, not all the components of Einstein equations are satisfied. We construct an improved energy-momentum tensor that consistently satisfies Einstein equations and show that it leads to a different prediction for the region where the strong energy condition is violated. For certain choice of parameters, our proposal predicts the violation of the energy condition outside the Cauchy horizon, which might be important for observational signatures.