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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2402.09539 |
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| _version_ | 1866914358027616256 |
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| author | Sahu, Abhisek |
| author_facet | Sahu, Abhisek |
| contents | We analyse spherically symmetric spacetimes obtained by gluing a cosmological region to a Schwarzschild black hole across a singular co-dimension one hypersurface. Assuming an arbitrary homogeneous and isotropic cosmology, and working in spacetime dimensions greater than three with general cosmological constant, we derive the stress-energy tensor required on the hypersurface directly in terms of the cosmological energy density. This general framework yields a new exact solution in four dimensions describing a radiation-filled cosmology matched to vacuum through a pressureless dust shell. A systematic exploration of parameter space reveals twenty-two distinct families of solutions, including bubble-of-cosmology and Swiss-cheese spacetimes with different global and causal structures. We also discuss possible generalisations of the construction and explain why such thin-shell cosmologies are of interest in the context of holography and quantum cosmology. For negative cosmological constant, a subset of these solutions admits a Euclidean continuation compatible with a holographic interpretation developed in related work. In addition, we provide a pedagogical introduction to hypersurfaces in general relativity and a practical framework for constructing thin-shell spacetimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09539 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singular hypersurfaces and thin shells in cosmology Sahu, Abhisek High Energy Physics - Theory General Relativity and Quantum Cosmology We analyse spherically symmetric spacetimes obtained by gluing a cosmological region to a Schwarzschild black hole across a singular co-dimension one hypersurface. Assuming an arbitrary homogeneous and isotropic cosmology, and working in spacetime dimensions greater than three with general cosmological constant, we derive the stress-energy tensor required on the hypersurface directly in terms of the cosmological energy density. This general framework yields a new exact solution in four dimensions describing a radiation-filled cosmology matched to vacuum through a pressureless dust shell. A systematic exploration of parameter space reveals twenty-two distinct families of solutions, including bubble-of-cosmology and Swiss-cheese spacetimes with different global and causal structures. We also discuss possible generalisations of the construction and explain why such thin-shell cosmologies are of interest in the context of holography and quantum cosmology. For negative cosmological constant, a subset of these solutions admits a Euclidean continuation compatible with a holographic interpretation developed in related work. In addition, we provide a pedagogical introduction to hypersurfaces in general relativity and a practical framework for constructing thin-shell spacetimes. |
| title | Singular hypersurfaces and thin shells in cosmology |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2402.09539 |