Quasinormal frequencies of D-dimensional Schwarzschild black holes: evaluation via continued fraction method

TL;DR

This paper extends Leaver's continued fraction method to compute quasinormal frequencies of higher-dimensional Schwarzschild black holes, addressing singularity challenges as the dimension increases, and provides specific frequency calculations for D=10, 11, and 9.

Contribution

It introduces a generalized approach for applying Leaver's method in higher dimensions with multiple singularities, enabling accurate frequency calculations where the original method fails.

Findings

Calculated gravitational quasinormal frequencies for D=10 and D=11.

Developed a continuation method to handle multiple singularities.

Provided detailed results for D=9, 10, and 11 dimensions.

Abstract

We adopt Leaver's method to determine quasi normal frequencies of the Schwarzschild black hole in higher (D >= 10) dimensions. In D-dimensional Schwarzschild metric, when D increases, more and more singularities, spaced uniformly on the unit circle |r|=1, approach the horizon at r = r_h = 1. Thus, a solution satisfying the outgoing wave boundary condition at the horizon must be continued to some mid point and only then the continued fraction condition can be applied. This prescription is general and applies to all cases for which, due to regular singularities on the way from the point of interest to the irregular singularity, Leaver's method in its original setting breaks down. We illustrate the method calculating gravitational vector and tensor quasinormal frequencies of the Schwarzschild black hole in D=11 and D=10 dimensions. We also give the details for the D=9 case, considered in gr-qc/0511064.