Graviton scattering on self-dual black holes

TL;DR

This paper computes exact gravitational wave scattering and MHV graviton amplitudes on self-dual black hole backgrounds using twistor theory and integrability, providing explicit formulas and analyzing spin effects.

Contribution

It introduces an exact solution for graviton scattering and MHV amplitudes on self-dual black holes, leveraging integrability and twistor methods.

Findings

Exact solutions for graviton scattering on self-dual black holes.

Explicit formulas for MHV graviton amplitudes at arbitrary multiplicity.

Holomorphic collinear splitting functions are unchanged from flat space.

Abstract

The computation of gravitational wave scattering on black hole spacetimes is an extremely hard problem, typically requiring approximation schemes that either treat the black hole perturbatively or are only amenable to numerical techniques. In this paper, we consider linearised gravitational waves (or gravitons) scattering on the self-dual analogue of a black hole: namely, the self-dual Taub-NUT metric. Using the hidden integrability of the self-dual sector, we solve the linearised Einstein equations on these self-dual black hole backgrounds exactly in terms of simple, explicit quasi-momentum eigenstates. Using a description of the self-dual Taub-NUT metric and its gravitons in terms of twistor theory, we obtain an explicit formula, exact in the background, for the tree-level maximal helicity violating (MHV) graviton scattering amplitude at arbitrary multiplicity, with and without spin. This is obtained from the description of the MHV amplitudes in terms of the perturbation theory of a chiral sigma model whose target is the twistor space of the background. The incorporation of spin effects on these backgrounds is a straightforward application of the Newman-Janis shift. We also demonstrate that the holomorphic collinear splitting functions in the self-dual background are equal to those in flat space so that the celestial symmetry algebra is undeformed.