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

TL;DR

This paper explores the mathematical connection between black hole scattering processes and Painlevé VI transcendents using isomonodromy methods, providing a novel approach to understanding black hole physics and quantum complementarity.

Contribution

It introduces a new method linking black hole scattering to Painlevé VI via isomonodromy, offering a Hamilton-Jacobi framework for calculating scattering amplitudes.

Findings

Connection between black hole scattering and Painlevé VI transcendent

Development of a Hamilton-Jacobi based computational method

Implications for black hole complementarity

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 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.