Kerr-de Sitter Greybody Factors via Isomonodromy

TL;DR

This paper derives scattering amplitudes for scalar fields in Kerr-de Sitter black holes using monodromy methods, linking conformal symmetry, Painlevé equations, and black hole physics.

Contribution

It introduces a novel monodromy technique to compute greybody factors in Kerr-de Sitter spacetimes, connecting conformal blocks with black hole scattering data.

Findings

Explicit expression for scattering amplitudes using monodromy parameters

Connection between Painlevé VI τ-function and black hole scattering

Verification of conformal symmetry's role in black hole physics

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 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.