论文标题
带有宇宙常数的真空空间中的Weyl双副本
The Weyl double copy in vacuum spacetimes with a cosmological constant
论文作者
论文摘要
我们使用我们先前描述的方法检查了以宇宙常数为基础的爱因斯坦方程真空溶液的Weyl双拷贝关系，其中旋转1/2无质量的自由田旋转器（Dirac-Weyl场）被视为基本单元。基于确切的非扭曲真空N型和真空D型溶液，该发现明确表明，单个和零件副本在同型平坦的时空中实现了共同不变的场方程。此外，不论存在宇宙常数如何，我们证明了零副本将dirac-weyl场与弯曲时空中的退化电磁场连接起来，此外还将重力场与单个副本中的单个副本连接起来。此外，该研究还证明了零副本在时间依赖性辐射溶液中的重要性。特别是，对于Robinson-Trautman（$λ$）的引力波，与单个副本不同，我们发现零副本具有其他信息来指定相关引力波的来源是至少在弱场限制中，是否是时间样，空或太空的源。
We examine the Weyl double copy relation for vacuum solutions of the Einstein equations with a cosmological constant using the approach we previously described, in which the spin-1/2 massless free-field spinors (Dirac-Weyl fields) are regarded as basic units. Based on the exact non-twisting vacuum type N and vacuum type D solutions, the finding explicitly shows that the single and zeroth copies fulfill conformally invariant field equations in conformally flat spacetime. In addition, irrespective of the presence of a cosmological constant, we demonstrate that the zeroth copy connects Dirac-Weyl fields with the degenerate electromagnetic fields in the curved spacetime in addition to connecting gravity fields with the single copy in conformally flat spacetime. Moreover, the study also demonstrates the critical significance the zeroth copy plays in time-dependent radiation solutions. In particular, for Robinson-Trautman ($Λ$) gravitational waves, unlike the single copy, we find that the zeroth copy carries additional information to specify whether the sources of associated gravitational waves are time-like, null, or space-like, at least in the weak field limit.
