The cosmological volume function
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914198056861696 |
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| author | García-Heveling, Leonardo |
| author_facet | García-Heveling, Leonardo |
| contents | In a previous work, the regular cosmological volume function $τ_V$ was introduced as an alternative to the regular cosmological time function of Andersson, Galloway, and Howard. In this paper, we show that in many cases of interest, $τ_V$ is a continuously differentiable temporal function. This leads to a canonical splitting of the metric tensor, and induces a canonical ``Wick-rotated" Riemannian metric. We also provide some further results and examples related to the cosmological time and volume functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11626 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The cosmological volume function García-Heveling, Leonardo General Relativity and Quantum Cosmology Differential Geometry 83F05 (primary) 53C50 (secondary) In a previous work, the regular cosmological volume function $τ_V$ was introduced as an alternative to the regular cosmological time function of Andersson, Galloway, and Howard. In this paper, we show that in many cases of interest, $τ_V$ is a continuously differentiable temporal function. This leads to a canonical splitting of the metric tensor, and induces a canonical ``Wick-rotated" Riemannian metric. We also provide some further results and examples related to the cosmological time and volume functions. |
| title | The cosmological volume function |
| topic | General Relativity and Quantum Cosmology Differential Geometry 83F05 (primary) 53C50 (secondary) |
| url | https://arxiv.org/abs/2512.11626 |