Asymptotic quasinormal modes of a noncommutative geometry inspired Schwarzschild black hole

TL;DR

This paper investigates the asymptotic quasi-normal modes of a noncommutative geometry inspired Schwarzschild black hole, revealing the influence of noncommutativity on the frequencies and their relation to Hawking temperature.

Contribution

It provides the first analysis of asymptotic quasi-normal modes for noncommutative inspired Schwarzschild black holes, including single and double horizon cases, highlighting the role of noncommutativity.

Findings

Real part of frequency proportional to ln(3)

Noncommutativity affects the proportionality constant via Hawking temperature

Both single and double horizon cases exhibit similar frequency behavior

Abstract

We study the asymptotic quasi-normal modes for the scalar perturbation of the non-commutative geometry inspired Schwarzschild black hole in (3+1) dimensions. We have considered $M\geq M_0$, which effectively correspond to a single horizon Schwarzschild black hole with correction due to non-commutativity. We have shown that for this situation the real part of the asymptotic quasi-normal frequency is proportional to $\ln (3)$. The effect of non-commutativity of spacetime on quasi-normal frequency arises through the constant of proportionality, which is Hawking temperature $T_H(\theta)$. We also consider the two horizon case and show that in this case also the real part of the asymptotic quasi-normal frequency is proportional to $\ln(3)$.