Quasinormal modes of dirty black holes in the effective theory of gravity with a third order curvature term

We consider the gravitational quasinormal modes of the static and spherically-symmetric dirty black holes in the effective theory of gravity with the third order curvature term inspired by the Goroff-Sagnotti calculation. It is demonstrated that using the WKB-Pad\'e summation proposed in [J. Matyjasek and M. Opala, Phys. Rev. D 96, 024011 (2017)] one can achieve sufficient accuracy to calculate corrections to the complex frequencies of the quasinormal modes caused by the Goroff-Sagnotti curvature term. It is shown that the curvature 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.

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