Five dimensional Weyl double copy

Abstract

The Weyl double copy (WDC) relation connects the Weyl tensor of the gravity theory and the field strength tensor of the Maxwell theory, which provides a concrete realization of the classical double copy. Although intensively investigated, the WDC is only limited in four-dimensional spacetime. In this Letter, we generalize the WDC relation to five-dimensional spacetime, which offers the first example of the WDC in higher dimensions. We show that a special class of five-dimensional type N vacuum solutions admits a special class of degenerate Maxwell field that squares to give the Weyl tensor. The five-dimensional WDC relation defines a scalar field that satisfies the source-free Klein-Gordon equation on the curved background. We further verify that for five-dimensional pp-wave solution and Kundt solutions, the Maxwell fields and the scalar fields also satisfy the Maxwell's equations and the wave equation on five-dimensional Minkowski spacetime.

v2: 10 pages + 4 appendixes, interpretations significantly improved, comments on the background for Maxwell and scalar fields added, refs. added, accepted for publication in PRD as a Letter