Topologies on the future causal completion
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866929630809686016 |
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| author | Müller, Olaf |
| author_facet | Müller, Olaf |
| contents | On the Geroch-Kronheimer-Penrose future completion $IP(X)$ of a spacetime $X$, there are two frequently used topologies. We systematically examine $τ_+$, the stronger (metrizable) of them, which is the coarsest causally continuous topology, obtaining a variety of novel results, among them a complete characterization of the difference in convergence between both topologies. In our framework, we can allow for $X$ being a chr. space and consequently for the interpretation of $IP$ as an idempotent functor on a category that includes spacetimes of very low regularity. Furthermore, we explicitly calculate $(IP(X), τ_+)$ for multiply warped chronological spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_03797 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Topologies on the future causal completion Müller, Olaf Differential Geometry 53C50 On the Geroch-Kronheimer-Penrose future completion $IP(X)$ of a spacetime $X$, there are two frequently used topologies. We systematically examine $τ_+$, the stronger (metrizable) of them, which is the coarsest causally continuous topology, obtaining a variety of novel results, among them a complete characterization of the difference in convergence between both topologies. In our framework, we can allow for $X$ being a chr. space and consequently for the interpretation of $IP$ as an idempotent functor on a category that includes spacetimes of very low regularity. Furthermore, we explicitly calculate $(IP(X), τ_+)$ for multiply warped chronological spaces. |
| title | Topologies on the future causal completion |
| topic | Differential Geometry 53C50 |
| url | https://arxiv.org/abs/1909.03797 |