Kerr–de Sitter greybody factors via isomonodromy

Abstract

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 ${\ensuremath{\sigma}}_{ij}$ between two regular singular points, can be solved implicitly in terms of the Painlev\'e VI $\ensuremath{\tau}$ 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.