Scattering on self-dual black holes

Abstract

Tree-level graviton scattering amplitudes provide an on-shell model for wave-wave scattering in general relativity, but computing them with traditional perturbative methods is hard due to the non-polynomial nature of the Einstein-Hilbert action. This is particularly true for graviton scattering in curved spacetimes, like black holes, which remains an extremely difficult problem. I will discuss a toy model of this problem: graviton scattering on a self-dual black hole (in particular, a self-dual Taub-NUT metric). This lets us bring powerful integrability methods to bear while still exhibiting the non-linear and non-perturbative hallmarks of 'real world' graviton scattering on black holes. Remarkably, in this setting it is possible to obtain explicit formulae for graviton scattering amplitudes which are exact in the background.