Solution for the Einstein-Maxwell equations invariant under an $(n - 1)$-dimensional group of dilations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911441324343296 |
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| author | Leandro, Benedito Menezes, Ilton Novais, Rafael |
| author_facet | Leandro, Benedito Menezes, Ilton Novais, Rafael |
| contents | We consider an electrostatic system whose spatial factor is conformal to an $n$-dimensional Euclidean space. We provide a complete characterization of the most general ansatz, thereby reducing the associated electrostatic system of partial differential equations to an ordinary differential equation system. We prove that there are only two possibilities: either the cosmological constant is nonzero, in which case the solutions are necessarily invariant under rotations or translations, or the cosmological constant vanishes, and the solutions belong to the Majumdar-Papapetrou class with a degree of freedom associated with an invariant $(n-1)$-dimensional subgroup. As a result, we introduce a new solution to the electrovacuum system in the Majumdar-Papapetrou class that is invariant under an $(n-1)$-dimensional group of dilations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11115 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solution for the Einstein-Maxwell equations invariant under an $(n - 1)$-dimensional group of dilations Leandro, Benedito Menezes, Ilton Novais, Rafael Differential Geometry Mathematical Physics Analysis of PDEs We consider an electrostatic system whose spatial factor is conformal to an $n$-dimensional Euclidean space. We provide a complete characterization of the most general ansatz, thereby reducing the associated electrostatic system of partial differential equations to an ordinary differential equation system. We prove that there are only two possibilities: either the cosmological constant is nonzero, in which case the solutions are necessarily invariant under rotations or translations, or the cosmological constant vanishes, and the solutions belong to the Majumdar-Papapetrou class with a degree of freedom associated with an invariant $(n-1)$-dimensional subgroup. As a result, we introduce a new solution to the electrovacuum system in the Majumdar-Papapetrou class that is invariant under an $(n-1)$-dimensional group of dilations. |
| title | Solution for the Einstein-Maxwell equations invariant under an $(n - 1)$-dimensional group of dilations |
| topic | Differential Geometry Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2602.11115 |