# Perturbing microscopic black holes inspired by noncommutativity

## TL;DR

This paper investigates the stability of microscopic noncommutative black holes by analyzing quasinormal modes, revealing that some observed instabilities are artifacts of the WKB approximation and demonstrating alternative methods for accurate analysis.

## Contribution

The study shows that WKB method instabilities are artifacts and introduces the asymptotic iteration method as a useful tool for calculating quasinormal modes of noncommutative black holes.

## Key findings

- WKB method does not converge in critical cases with instabilities.
- Instabilities are artifacts of the WKB approximation.
- Asymptotic iteration method effectively finds quasinormal modes.

## Abstract

We probe into the instabilities of microscopic quantum black holes. For this purpose, we study the quasinormal modes (QNMs) for a massless scalar perturbation of the noncommutative geometry inspired Schwarzschild black hole. By means of a sixth order Wentzel-Kramers-Brillouin (WKB) approximation we show that the widely used WKB method does not converge in the critical cases where instabilities show up at the third order. By employing the inverted potential method, we demonstrate that the instabilities are an artifact of the WKB method. Finally, we discuss the usefulness of the asymptotic iteration method to find the QNMs.