Solving Einstein's Equation Numerically on Manifolds with Non-Orientable Spatial Slices
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908991517360128 |
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| author | Zhang, Fan Lindblom, Lee |
| author_facet | Zhang, Fan Lindblom, Lee |
| contents | This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been constructed on a selection of manifolds having positive, negative, and vanishing spatial scalar curvatures. One example is shown to be indistinguishable locally from a homogeneous Friedman cosmological model, others are constructed with significant inhomogeneities. Together these examples are used to explore the strengths and the limitations of the numerical methods used in this study, and to test the code used to implement them. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_22954 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solving Einstein's Equation Numerically on Manifolds with Non-Orientable Spatial Slices Zhang, Fan Lindblom, Lee General Relativity and Quantum Cosmology This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been constructed on a selection of manifolds having positive, negative, and vanishing spatial scalar curvatures. One example is shown to be indistinguishable locally from a homogeneous Friedman cosmological model, others are constructed with significant inhomogeneities. Together these examples are used to explore the strengths and the limitations of the numerical methods used in this study, and to test the code used to implement them. |
| title | Solving Einstein's Equation Numerically on Manifolds with Non-Orientable Spatial Slices |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.22954 |