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 σ between the inner and the outer horizons. Using the isomonodromy flow, we calculate σ exactly in terms of the Painlevé V τ -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 τ -function to Liouville irregular conformal blocks to claim that this scattering problem is solved in the combinatorial sense, with known expressions for the τ -function near the critical points.
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da Cunha, B.C., Novaes, F. Kerr scattering coefficients via isomonodromy. J. High Energ. Phys. 2015, 144 (2015). https://doi.org/10.1007/JHEP11(2015)144
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DOI: https://doi.org/10.1007/JHEP11(2015)144