Kerr-de Sitter Greybody Factors via Isomonodromy

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 non-trivial parameter, the composite monodromy parameter $\sigma_{ij}$ between two regular singular points, can be solved implicitily in terms of the Painlev\'e VI $\tau$-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.