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arXiv · 2407.18791

The vacuum weighted Einstein field equations

M. Brozos-Vázquez·D. Mojón-Álvarez
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Abstract

On a spacetime $(M,g)$ endowed with a density function $h$, we consider the vacuum weighted Einstein field equations: \[h\rho-\operatorname{Hes}_h+\Delta h g=0.\] First, it is shown that the equation characterizes critical metrics for an appropriate action. Then, after describing locally conformally flat solutions in arbitrary dimension, four-dimensional solutions with harmonic curvature are classified.

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M. Brozos-Vázquez, D. Mojón-Álvarez. 2024-07-26. The vacuum weighted Einstein field equations. https://arxiv.org/abs/2407.18791

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