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

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-Padé 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.