Volume-distance-ratio asymptote and spacetime inextendibility for spatially flat and hyperbolic FLRW spacetimes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915436656852992 |
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| author | Le, Pengyu |
| author_facet | Le, Pengyu |
| contents | We study the volume-distance-ratio (VDR) asymptote at the past timelike boundary point for spatially flat FLRW spacetime with scale factor $a(t) = t^α$, and spatially hyperbolic FLRW spacetime with scale factor $a(t) = a_0 t^α$. We employ the spacetime inextendibility criteria via the volume-distance-ratio asymptote to deduce their inextendibility. We show that for spatial dimensions greater than $2$, there exists at least one critical exponent $α\in (0,1)$ for which the VDR asymptote along the $Σ_t$-orthogonal geodesic equals the Minkowski value. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Volume-distance-ratio asymptote and spacetime inextendibility for spatially flat and hyperbolic FLRW spacetimes Le, Pengyu General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry 83C75 (Primary) 83F05, 53B30, 35A21 (Secondary) We study the volume-distance-ratio (VDR) asymptote at the past timelike boundary point for spatially flat FLRW spacetime with scale factor $a(t) = t^α$, and spatially hyperbolic FLRW spacetime with scale factor $a(t) = a_0 t^α$. We employ the spacetime inextendibility criteria via the volume-distance-ratio asymptote to deduce their inextendibility. We show that for spatial dimensions greater than $2$, there exists at least one critical exponent $α\in (0,1)$ for which the VDR asymptote along the $Σ_t$-orthogonal geodesic equals the Minkowski value. |
| title | Volume-distance-ratio asymptote and spacetime inextendibility for spatially flat and hyperbolic FLRW spacetimes |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry 83C75 (Primary) 83F05, 53B30, 35A21 (Secondary) |
| url | https://arxiv.org/abs/2508.03263 |