The mystery of the asymptotic quasinormal modes of Gauss-Bonnet black holes with small Gauss-Bonnet coupling

TLDR: In this article, the quasinormal modes of D-dimensional Schwarzschild black holes with the Gauss-Bonnet correction in the large damping limit were analyzed and it was shown that standard analytic techniques cannot be applied in a straightforward manner to the case of infinite damping.

Abstract: We analyse the quasinormal modes of D-dimensional Schwarzschild black holes with the Gauss–Bonnet correction in the large damping limit and show that standard analytic techniques cannot be applied in a straightforward manner to the case of infinite damping. However, by using a combination of analytic and numeric techniques, which can only be applied to vector perturbations, we are able to calculate the quasinormal mode frequencies of vector perturbations for a range where the damping is large but finite. We show that in this 'intermediate' damping region, the famous ln(3) appears in the real part of the quasinormal mode frequency. In our calculations, the Gauss–Bonnet coupling, α, is taken to be much smaller than the parameter μ, which is related to the black hole mass. Even though our calculations are done for the simplest case of five spacetime dimensions, it is shown that the results hold in every dimension greater than four by substituting an approximate expression for the metric in the calculations, which is valid in the intermediate damping region for small α.