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Scattering data can be generically described in terms of monodromies. Here we obtain scattering amplitudes for conformally coupled scalar fields in Kerr--de Sitter black holes using this monodromy technique. The only nontrivial parameter, the composite monodromy parameter ₈₉ between two regular singular points, can be solved implicitly in terms of the Painlev\'e VI function. The application of the Virasoro conformal blocks to solve the latter can now be interpreted as a verification of the striking relationship between conformal symmetry and black holes.
Cunha et al. (Tue,) studied this question.