Quasinormal modes for tensor and vector type perturbation of Gauss Bonnet black holes using third order WKB approach

TL;DR

This paper calculates quasinormal modes of Gauss-Bonnet black holes in various dimensions using third order WKB, revealing how frequencies depend on coupling, charge, and perturbation type, and clarifying discrepancies in previous results.

Contribution

It provides new calculations of quasinormal modes for tensor and vector perturbations of Gauss-Bonnet black holes across multiple dimensions using third order WKB, including charged cases and addressing previous inconsistencies.

Findings

Real part of QN frequencies increases with Gauss-Bonnet coupling.

Imaginary part of QN frequencies first decreases then increases with coupling.

QN frequencies for scalar and tensor perturbations differ, especially at higher coupling.

Abstract

We obtain the quasinormal modes for tensor perturbations of Gauss-Bonnet (GB) black holes in $d=5, 7, 8$ dimensions and vector perturbations in $d = 5, 6, 7$ and 8 dimensions using third order WKB formalism. The tensor perturbation for black holes in $d=6$ is not considered because of the fact that it is unstable to tensor mode perturbations. In the case of uncharged GB black hole, for both tensor and vector perturbations, the real part of the QN frequency increases as the Gauss-Bonnet coupling ($\alpha'$) increases. The imaginary part first decreases upto a certain value of $\alpha'$ and then increases with $\alpha'$ for both tensor and vector perturbations. For larger values of $\alpha'$, the QN frequencies for vector perturbation differs slightly from the QN frequencies for tensorial one. It has also been shown that as $\alpha' \to 0$, the quasinormal mode frequency for tensor and vector perturbation of the Schwarzschild black hole can be obtained. We have also calculated the quasinormal spectrum of the charged GB black hole for tensor perturbations. Here we have found that the real oscillation frequency increases, while the imaginary part of the frequency falls with the increase of the charge. We also show that the quasinormal frequencies for scalar field perturbations and the tensor gravitational perturbations do not match as was claimed in the literature. The difference in the result increases if we increase the GB coupling.