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| Format: | Preprint |
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2023
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| Online-Zugang: | https://arxiv.org/abs/2311.06927 |
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| _version_ | 1866917764643422208 |
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| author | Vigneron, Quentin Szabó, Áron Mourier, Pierre |
| author_facet | Vigneron, Quentin Szabó, Áron Mourier, Pierre |
| contents | Vigneron [Foundations of Physics, 54, 15, (2024)] recently proposed a modification of general relativity in which a non-dynamical term related to the spatial topology is introduced in the Einstein equation. The original motivation for this theory is to allow for the non-relativistic limit to exist in any physical topology. In the present paper, we derive a first inhomogeneous exact vacuum solution of this theory for a spherical topology, assuming staticity and spherical symmetry. The metric represents a black hole and a repulsive singularity at opposite poles of a 3-sphere. The solution is similar to the Schwarzschild metric, but the spacelike infinity is cut, and replaced by a repulsive singularity at finite distance, implying that the spacelike hypersurfaces have finite volume, and the total mass is zero. We discuss how this solution paves the way to massive, non-static solutions of this theory, more directly relevant for cosmology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_06927 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topologically modified Einstein equation: a solution with singularities on $\mathbb{S}^3$ Vigneron, Quentin Szabó, Áron Mourier, Pierre General Relativity and Quantum Cosmology Vigneron [Foundations of Physics, 54, 15, (2024)] recently proposed a modification of general relativity in which a non-dynamical term related to the spatial topology is introduced in the Einstein equation. The original motivation for this theory is to allow for the non-relativistic limit to exist in any physical topology. In the present paper, we derive a first inhomogeneous exact vacuum solution of this theory for a spherical topology, assuming staticity and spherical symmetry. The metric represents a black hole and a repulsive singularity at opposite poles of a 3-sphere. The solution is similar to the Schwarzschild metric, but the spacelike infinity is cut, and replaced by a repulsive singularity at finite distance, implying that the spacelike hypersurfaces have finite volume, and the total mass is zero. We discuss how this solution paves the way to massive, non-static solutions of this theory, more directly relevant for cosmology. |
| title | Topologically modified Einstein equation: a solution with singularities on $\mathbb{S}^3$ |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2311.06927 |