Effects of non-commutative geometry on black hole properties

TL;DR

This paper explores how non-commutative geometry influences black hole characteristics, including thermodynamics, quasinormal modes, and gravitational lensing, providing new analytical insights into their behavior and observable signatures.

Contribution

It offers a comprehensive analysis of non-commutative black holes, calculating thermodynamic properties, quasinormal modes, and lensing effects with novel analytical and numerical methods.

Findings

Black hole lifetime is analytically derived with grey-body factors.

Thermodynamic quantities like entropy and heat capacity are computed for non-commutative black holes.

Deflection angles are analyzed in weak and strong gravitational lensing regimes.

Abstract

In this study, we investigate the signatures of a non-commutative black hole solution. Initially, we calculate the thermodynamic properties of the system, including entropy, heat capacity, and Hawking radiation. For the latter quantity, we employ two distinct methods: surface gravity and the topological approach. Additionally, we examine the emission rate and remnant mass within this context. Remarkably, the lifetime of the black hole, after reaching its final state due to the evaporation process, is expressed analytically up to a grey-body factor. We estimate the lifetime for specific initial and final mass configurations. Also, we analyze the tensorial quasinormal modes using the 6th-order WKB method. Finally, we study the deflection angle, i.e., gravitational lensing, in both the weak and strong deflection limits.