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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.11956 |
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| _version_ | 1866912839561641984 |
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| author | Minguzzi, Ettore |
| author_facet | Minguzzi, Ettore |
| contents | The properties of the stable distance over stable spacetimes are used as a reference to propose a simplified, abstract notion of spacetime. The discussion shows that spacetime, with its topology, causal order and (upper semi-continuous) Lorentzian distance, can be introduced in a general and minimalistic way. Specifically, it is shown that spacetime can be represented as nothing more than a family of functions defined over an arbitrary set, the functions being a posteriori interpreted as rushing time functions. The proof makes use of the product trick which reduces causality and metricity to causality in a space with one additional dimension, so leading to a kind of unification for the notions of time function and proper time. Ultimately, our results show that time fully characterizes spacetime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The representation of spacetime through time functions Minguzzi, Ettore General Relativity and Quantum Cosmology The properties of the stable distance over stable spacetimes are used as a reference to propose a simplified, abstract notion of spacetime. The discussion shows that spacetime, with its topology, causal order and (upper semi-continuous) Lorentzian distance, can be introduced in a general and minimalistic way. Specifically, it is shown that spacetime can be represented as nothing more than a family of functions defined over an arbitrary set, the functions being a posteriori interpreted as rushing time functions. The proof makes use of the product trick which reduces causality and metricity to causality in a space with one additional dimension, so leading to a kind of unification for the notions of time function and proper time. Ultimately, our results show that time fully characterizes spacetime. |
| title | The representation of spacetime through time functions |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2508.11956 |