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

Abstract

We consider the dimensional reduction to two dimensions of certain gravitational theories in $D\ge 4$ 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.

54 pages; v2: references added

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Cited by in corpus (1)

• Solving gravitational field equations by Wiener-Hopf matrix factorisation, and beyond