Quasinormal modes of Gauss-Bonnet black holes at large D

TL;DR

This paper investigates the quasinormal modes of Gauss-Bonnet black holes in the large D limit, revealing how the modes are affected by the GB parameter and identifying new features at large values.

Contribution

It provides the first analysis of quasinormal modes of Gauss-Bonnet black holes at large D, including analytical and numerical results for different GB parameter regimes.

Findings

Non-decoupling modes match Schwarzschild case when GB parameter is small

Decoupled modes are slightly modified by the GB term at small GB parameter

New non-decoupling modes emerge at large GB parameter due to a new potential plateau

Abstract

Einstein's General Relativity theory simplifies dramatically in the limit that the spacetime dimension D is very large. This could still be true in the gravity theory with higher derivative terms. In this paper, as the first step to study the gravity with a Gauss-Bonnet(GB) term, we compute the quasi-normal modes of the spherically symmetric GB black hole in the large D limit. When the GB parameter is small, we find that the non-decoupling modes are the same as the Schwarzschild case and the decoupled modes are slightly modified by the GB term. However, when the GB parameter is large, we find some novel features. We notice that there are another set of non-decoupling modes due to the appearance of a new plateau in the effective radial potential. Moreover, the effective radial potential for the decoupled vector-type and scalar-type modes becomes more complicated. Nevertheless we manage to compute the frequencies of the these decoupled modes analytically. When the GB parameter is neither very large nor very small, though analytic computation is not possible, the problem is much simplified in the large D expansion and could be numerically treated. We study numerically the vector-type quasinormal modes in this case.