Isomonodromy, Painlev\'e Transcendents and Scattering off of Black Holes

Understand

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 Painlev\'e VI transcendent.
• We review a few facts about Painlev\'e 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 Painlev\'e, and discuss the implications of the generic result to black hole complementarity.