The Weyl Double Copy for Gravitational Waves

Godazgar, Hadi; Godazgar, Mahdi; Monteiro, Ricardo; Pope, C. N.; Veiga, David Peinador

doi:10.1103/PhysRevLett.126.101103

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The Weyl Double Copy for Gravitational Waves

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Godazgar, Hadi
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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2010.02925.pdf
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Citation

Godazgar, H., Godazgar, M., Monteiro, R., Pope, C. N., & Veiga, D. P. (2021). The Weyl Double Copy for Gravitational Waves. Physical Review Letters, 126(10 ): 101103. doi:10.1103/PhysRevLett.126.101103.

Cite as: https://hdl.handle.net/21.11116/0000-0007-4E7A-A

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. The converse statement also
holds, i.e. if there exists a degenerate Maxwell field on a curved background,
then the background is type N. 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.