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We consider gravitational quasinormal modes of the static andspherically-symmetric dirty black holes in the effective theory of gravitywhich is renormalizable at the two-loop level. It is demonstrated that usingthe WKB-Pad\'e summation proposed in \cite{jaOp} one can achieve sufficientaccuracy to calculate corrections to the complex frequencies of the quasinormalmodes caused by the Goroff-Sagnotti curvature terms. It is shown that theGoroff-Sagnotti correction (with our choice of the sign of the couplingconstant) increases damping of the fundamental modes (except for the lowestfundamental mode) and decreases their frequencies. We argue that the methodsadopted in this paper can be used in the analysis of the influence of thehigher-order curvature terms upon the quasinormal modes and in a number ofrelated problems that require high accuracy.

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