Kerr Scattering Coefficients via Isomonodromy

Abstract

We study the scattering of a massless scalar field in a generic Kerr background. Using a particular gauge choice based on the current conservation of the radial equation, we give a generic formula for the scattering coefficient in terms of the composite monodromy parameter $\sigma$ between the inner and the outer horizons. Using the isomonodromy flow, we calculate $\sigma$ exactly in terms of the Painlevé V $\tau$-function. We also show that the eigenvalue problem for the angular equation (spheroidal harmonics) can be calculated using the same techniques. We use recent developments relating the Painlevé V $\tau$-function to Liouville irregular conformal blocks to claim that this scattering problem is solved in the combinatorial sense, with known expressions for the $\tau$-function near the critical points.

version accepted at JHEP, JHEP style, 23 pages. Major revision with overall rewriting and including discussion about the angular equation and asymptotics of wavefunctions

References in corpus (3)

• Kerr-de Sitter Greybody Factors via Isomonodromy
• Asymptotic Spectroscopy of Rotating Black Holes
• Greybody factors at large imaginary frequencies

Cited by in corpus (1)

• Exploring the BTZ bulk with boundary conformal blocks