RESUMO
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.
RESUMO
We present a method for finding, in principle, all asymptotic gravitational charges. The basic idea is that one must consider all possible contributions to the action that do not affect the equations of motion for the theory of interest; such terms include topological terms. As a result we observe that the first order formalism is best suited to an analysis of asymptotic charges. In particular, this method can be used to provide a Hamiltonian derivation of recently found dual charges.