The absorption cross section of Reissner-Nordstr\"om black holes for the gravitational field is computed numerically, taking into account the coupling of the electromagnetic and gravitational perturbations. Our results are in excellent agreement with low- and high-frequency approximations. We find equality between gravitational and electromagnetic absorption cross sections of extreme Reissner-Nordstr\"om black holes for all frequencies, which we explain analytically. This gives the first example of objects in general relativity in four dimensions that absorb the electromagnetic and gravitational waves in exactly the same way.
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Oliveira et al. (2011) studied this question.