Abstract
We establish the status of the Weyl double copy relation for radiative solutions of the vacuum Einstein equations. We show that all type vacuum solutions, which describe the radiation region of isolated gravitational systems with appropriate falloff for the matter fields, admit a degenerate Maxwell field that squares to give the Weyl tensor. The converse statement also holds, i.e., if there exists a degenerate Maxwell field on a curved background, then the background is type . This relation defines a scalar that satisfies the wave equation on the background. We show that for nontwisting radiative solutions, the Maxwell field and the scalar also satisfy the Maxwell equation and the wave equation on Minkowski spacetime. Hence, nontwisting solutions have a straightforward double copy interpretation.
- Received 20 October 2020
- Revised 21 December 2020
- Accepted 17 February 2021
DOI:https://doi.org/10.1103/PhysRevLett.126.101103
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society