Spatially homogeneous solutions of vacuum Einstein equations in general dimensions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917920378978304 |
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| author | Sato, Yuichiro Tsuyuki, Takanao |
| author_facet | Sato, Yuichiro Tsuyuki, Takanao |
| contents | We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally hyperbolic spacetimes in which almost Abelian Lie groups act on the spaces isometrically and simply transitively. We give left-invariant metrics on the spaces and solve Ricci-flat conditions of the spacetimes. In the four-dimensional case, our solutions correspond to the Bianchi type II solution. By our results and previous studies, all spatially homogeneous solutions whose spaces have zero-dimensional moduli spaces of left-invariant metrics are found. For the simplest solution, we show that each of the spatial dimensions cannot expand or contract simultaneously in the late-time it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10193 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spatially homogeneous solutions of vacuum Einstein equations in general dimensions Sato, Yuichiro Tsuyuki, Takanao General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry 83E15 (Primary), 53B30 (Secondary) We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally hyperbolic spacetimes in which almost Abelian Lie groups act on the spaces isometrically and simply transitively. We give left-invariant metrics on the spaces and solve Ricci-flat conditions of the spacetimes. In the four-dimensional case, our solutions correspond to the Bianchi type II solution. By our results and previous studies, all spatially homogeneous solutions whose spaces have zero-dimensional moduli spaces of left-invariant metrics are found. For the simplest solution, we show that each of the spatial dimensions cannot expand or contract simultaneously in the late-time it. |
| title | Spatially homogeneous solutions of vacuum Einstein equations in general dimensions |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry 83E15 (Primary), 53B30 (Secondary) |
| url | https://arxiv.org/abs/2304.10193 |