The Weyl Double Copy for Gravitational Waves

TL;DR

This paper demonstrates that all type N vacuum solutions describing gravitational radiation can be related to Maxwell fields via the Weyl double copy, with simplified interpretations for non-twisting solutions.

Contribution

It establishes the Weyl double copy relation for radiative vacuum solutions, linking gravitational radiation to Maxwell fields and scalar wave equations.

Findings

Type N vacuum solutions admit a Maxwell field that squares to the Weyl tensor.

Non-twisting solutions have Maxwell and scalar fields satisfying equations on Minkowski space.

The scalar associated with the double copy satisfies the wave equation.

Abstract

We establish the status of the Weyl double copy relation for radiative solutions of the vacuum Einstein equations. We show that all type N vacuum solutions, which describe the radiation region of isolated gravitational systems with appropriate fall-off for the matter fields, admit a degenerate Maxwell field that squares to give the Weyl tensor. This relation defines a scalar that satisfies the wave equation on the background. We show that for non-twisting radiative solutions, the Maxwell field and the scalar also satisfy the Maxwell equation and the wave equation on Minkowski spacetime. Hence, non-twisting solutions have a straightforward double copy interpretation.