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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.18791 |
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Table of Contents:
- On a spacetime $(M,g)$ endowed with a density function $h$, we consider the vacuum weighted Einstein field equations: \[hρ-\operatorname{Hes}_h+Δh g=0.\] 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.