2024/07/15 by Brozos-Vázquez, Miguel, Mojón-Álvarez, Diego
#53B30 #53C21 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2407.10535
We classify solutions of the vacuum weighted Einstein field equations on smooth metric measure spacetimes (M,g,h dvolg) of dimension 4, where the underlying manifold (M,g) is a pr-wave. We use this result to provide examples of solutions with some special geometric properties. The gradient ∇ h is lightlike or spacelike. In the first case, the underlying manifold is a pp-wave. In the second case, the Ricci operator is nilpotent. Moreover, 2-step nilpotent solutions are also realized on pp-waves.