Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy

TL;DR

This paper develops a new single copy prescription linking gravitational solutions in Weyl-Lewis-Papapetrou coordinates to self-dual Yang-Mills equations, revealing the gauge group's role in encoding gravitational information.

Contribution

It introduces a novel single copy approach that incorporates non-trivial gauge group data, extending previous methods and applying it to various gravitational solutions.

Findings

Gauge group encodes gravitational solution details

Constructed single copy for multiple gravitational solutions

Established relation between gravitational and Yang-Mills equations

Abstract

We consider the dimensional reduction to two dimensions of certain gravitational theories in $D \geq 4$ dimensions at the two-derivative level. It is known that the resulting field equations describe an integrable system in two dimensions which can also be obtained by a dimensional reduction of the self-dual Yang-Mills equations in four dimensions. We use this relation to construct a single copy prescription for classes of gravitational solutions in Weyl-Lewis-Papapetrou coordinates. In contrast with previous proposals, we find that the gauge group of the Yang-Mills single copy carries non-trivial information about the gravitational solution. We illustrate our single copy prescription with various examples that include the extremal Reissner-Nordstrom solution, the Kaluza-Klein rotating attractor solution, the Einstein-Rosen wave solution and the self-dual Kleinian Taub-NUT solution.