Isomonodromy, Painlevé Transcendents and Scattering off of Black Holes
arXiv:1404.5188 · doi:10.1007/JHEP07(2014)132
Abstract
We apply the method of isomonodromy to study the scattering of a generic Kerr-NUT-(A)dS black hole. For generic values of the charges, the problem is related to the connection problem of the Painlevé VI transcendent. We review a few facts about Painlevé VI, Garnier systems and the Hamiltonian structure of flat connections in the Riemann sphere. We then outline a method for computing the scattering amplitudes based on Hamilton-Jacobi structure of Painlevé, and discuss the implications of the generic result to black hole complementarity.
40 pages, 4 figures, JHEP style