Quasinormal modes of dirty black holes in the two-loop renormalizable effective gravity

TL;DR

This paper calculates how two-loop renormalizable effective gravity corrections, specifically Goroff-Sagnotti terms, affect the quasinormal modes of static, spherically symmetric black holes, showing increased damping and decreased frequencies.

Contribution

It introduces a high-accuracy method using WKB-Padé summation to compute quasinormal mode corrections due to higher-order curvature terms in effective gravity.

Findings

Goroff-Sagnotti corrections increase damping of fundamental modes

These corrections decrease the frequencies of the modes

The method achieves high accuracy in calculating mode corrections

Abstract

We consider gravitational quasinormal modes of the static and spherically-symmetric dirty black holes in the effective theory of gravity which is renormalizable at the two-loop level. It is demonstrated that using the WKB-Pad\'e summation proposed in \cite{jaOp} one can achieve sufficient accuracy to calculate corrections to the complex frequencies of the quasinormal modes caused by the Goroff-Sagnotti curvature terms. It is shown that the Goroff-Sagnotti correction (with our choice of the sign of the coupling constant) increases damping of the fundamental modes (except for the lowest fundamental mode) and decreases their frequencies. We argue that the methods adopted in this paper can be used in the analysis of the influence of the higher-order curvature terms upon the quasinormal modes and in a number of related problems that require high accuracy.