Scalar-gravitational perturbations and quasinormal modes in the five dimensional Schwarzschild black hole

TL;DR

This paper computes quasinormal modes for gravitational perturbations of a five-dimensional Schwarzschild black hole using a continued fraction method, revealing distinct frequencies for different perturbation types and asymptotic behaviors at high mode numbers.

Contribution

It provides the first detailed calculation of QNMs for all perturbation types in 5D Schwarzschild black holes, highlighting differences and asymptotic properties.

Findings

Different QNM frequencies for scalar, vector, and tensor perturbations with same l

No purely imaginary QNM frequencies found

Asymptotic QNM behavior matches log3 + i2pi(n+1/2) in Hawking temperature units

Abstract

We calculate the quasinormal modes (QNMs) for gravitational perturbations of the Schwarzschild black hole in the five dimensional (5D) spacetime with a continued fraction method. For all the types of perturbations (scalar-gravitational, vector-gravitational, and tensor-gravitational perturbations), the QNMs associated with l=2, l=3, and l=4 are calculated. Our numerical results are summarized as follows: (i) The three types of gravitational perturbations associated with the same angular quantum number l have a different set of the quasinormal (QN) frequencies; (ii) There is no purely imaginary frequency mode; (iii) The three types of gravitational perturbations have the same asymptotic behavior of the QNMs in the limit of the large imaginary frequencies. In Hawking temperature units these frequencies are given by log3 + i2pi(n+1/2) as n goes to infinity, where n is the mode number.