AI Article Synopsis
- The study confirms the Weyl double copy relation for certain vacuum Einstein equations, particularly type N solutions, showing they can be linked to a degenerate Maxwell field.
- If a degenerate Maxwell field exists on a curved background, that background is classified as type N, establishing a two-way connection.
- For nontwisting radiative solutions, both the Maxwell field and a specific scalar satisfy important equations, allowing for a clear interpretation of the double copy in simpler Minkowski spacetime.
Article 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 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 N. 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.
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| http://dx.doi.org/10.1103/PhysRevLett.126.101103 | DOI Listing |
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