Scalar field quasinormal modes of noncommutative high dimensional Schwarzschild-Tangherlini black hole spacetime with smeared matter sources

TL;DR

This paper analyzes the quasinormal modes of massless scalar fields around noncommutative high-dimensional Schwarzschild-Tangherlini black holes using multiple methods, revealing the reliability of the 3rd order WKB approximation and exploring parameter effects.

Contribution

It provides a detailed analysis of scalar QNM frequencies in noncommutative high-dimensional black holes, comparing approximation methods and studying parameter influences.

Findings

High order WKB approximation often fails to converge for QNMs.

3rd WKB approximation is more reliable, confirmed by AIM and IPM methods.

Scalar QNM frequencies depend on noncommutative parameter, matter distribution, and dimension.

Abstract

We investigate the massless scalar quasinormal modes (QNMs) of the noncommutative $D$-dimensional Schwarzschild-Tangherlini black hole spacetime in this paper. By using the Wentzel-Kramers-Brillouin (WKB) approximation method, the asymptotic iterative method (AIM) and the inverted potential method (IPM) method, we made a detail analysis of the massless scalar QNM frequencies by varying the general smeared matter distribution and the allowable characteristic parameters ($k$ and $\theta$) corresponding to different dimensions. It is found that the nonconvergence of the high order WKB approximation exists in the QNMs frequencies of scalar perturbation around the noncommutative $D$-dimensional Schwarzschild black holes. We conclude that the 3rd WKB result should be more reliable than those of the high order WKB method since our numerical results are also verified by the AIM method and the IPM method. In the dimensional range of $4\leq D \leq7$, the scalar QNMs as a function of the different papameters (the noncommutative parameter $\theta$, the smeared matter distribution parameter $k$, the multipole number $l$ and the main node number $n$) are obtained. Moreover, we study the dynamical evolution of a scalar field in the background of the noncommutative high dimensional Schwarzschild-Tangherlini black hole.