The vacuum weighted Einstein field equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914888717172736 |
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| author | Brozos-Vázquez, M. Mojón-Álvarez, D. |
| author_facet | Brozos-Vázquez, M. Mojón-Álvarez, D. |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The vacuum weighted Einstein field equations Brozos-Vázquez, M. Mojón-Álvarez, D. Differential Geometry General Relativity and Quantum Cosmology 53B30 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. |
| title | The vacuum weighted Einstein field equations |
| topic | Differential Geometry General Relativity and Quantum Cosmology 53B30 |
| url | https://arxiv.org/abs/2407.18791 |