Godazgar Hadi, Godazgar Mahdi, Monteiro Ricardo, Veiga David Peinador, Pope C N
Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Mühlenberg 1, D-14476 Potsdam, Germany.
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom.
Phys Rev Lett. 2021 Mar 12;126(10):101103. doi: 10.1103/PhysRevLett.126.101103.
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.
我们确立了真空爱因斯坦方程辐射解的外尔双重拷贝关系的地位。我们表明，所有N型真空解，它们描述了具有适当物质场衰减的孤立引力系统的辐射区域，都允许一个退化的麦克斯韦场，其平方给出外尔张量。反之亦然，即如果在弯曲背景上存在一个退化的麦克斯韦场，那么该背景是N型的。这种关系定义了一个在背景上满足波动方程的标量。我们表明，对于非扭曲辐射解，麦克斯韦场和标量也满足闵可夫斯基时空上的麦克斯韦方程和波动方程。因此，非扭曲解具有直接的双重拷贝解释。
