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arXiv · 2407.10535

The vacuum weighted Einstein field equations on pr-waves

Miguel Brozos-Vázquez·Diego Mojón-Álvarez
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Abstract

We classify solutions of the vacuum weighted Einstein field equations on smooth metric measure spacetimes $(M,g,h\, dvol_g)$ 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 $\nabla h$ 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.

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Miguel Brozos-Vázquez, Diego Mojón-Álvarez. 2024-07-15. The vacuum weighted Einstein field equations on pr-waves. https://arxiv.org/abs/2407.10535

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