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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.19403 |
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| _version_ | 1866911226675593216 |
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| author | Surya, Sumati |
| author_facet | Surya, Sumati |
| contents | We construct a family of closeness functions on the space of finite volume Lorentzian geometries using the abundance of discrete intervals in the underlying random causal sets. Although strictly weaker than a Lorentzian Gromov-Hausdorff distance function, it has the advantage of being numerically calculable for large causal sets. It thus provides a concrete and quantitative measure of continuumlike behaviour in causal set theory and can be used to define a weak convergence condition for Lorentzian geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19403 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Closeness Function on Coarse Grained Lorentzian Geometries Surya, Sumati General Relativity and Quantum Cosmology We construct a family of closeness functions on the space of finite volume Lorentzian geometries using the abundance of discrete intervals in the underlying random causal sets. Although strictly weaker than a Lorentzian Gromov-Hausdorff distance function, it has the advantage of being numerically calculable for large causal sets. It thus provides a concrete and quantitative measure of continuumlike behaviour in causal set theory and can be used to define a weak convergence condition for Lorentzian geometries. |
| title | A Closeness Function on Coarse Grained Lorentzian Geometries |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2510.19403 |