Cosmic Censorship near FLRW spacetimes with negative spatial curvature
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916810044997632 |
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| author | Fajman, David Urban, Liam |
| author_facet | Fajman, David Urban, Liam |
| contents | We consider general initial data for the Einstein scalar-field system on a closed $3$-manifold $(M,γ)$ which is close to data for a Friedman-Lemaître-Robertson-Walker solution with homogeneous scalar field matter and a negative Einstein metric $γ$ as spatial geometry. We prove that the maximal globally hyperbolic development of such initial data in the Einstein scalar-field system is past incomplete in the contracting direction and exhibits stable collapse into a Big Bang curvature singularity. Under an additional condition on the first positive eigenvalue of $-Δ_γ$ satisfied, for example, by closed hyperbolic 3-manifolds of small diameter, we prove that the data evolves to a future complete spacetime in the expanding direction which asymptotes to a vacuum Friedman solution with $(M,γ)$ as the expansion normalized spatial geometry. In particular, the Strong Cosmic Censorship conjecture holds for this class of solutions in the $C^{2}$-sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_08052 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Cosmic Censorship near FLRW spacetimes with negative spatial curvature Fajman, David Urban, Liam General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs 83C75 (Primary), 35B35, 35Q76, 83C05, 83F05 (Secondary) We consider general initial data for the Einstein scalar-field system on a closed $3$-manifold $(M,γ)$ which is close to data for a Friedman-Lemaître-Robertson-Walker solution with homogeneous scalar field matter and a negative Einstein metric $γ$ as spatial geometry. We prove that the maximal globally hyperbolic development of such initial data in the Einstein scalar-field system is past incomplete in the contracting direction and exhibits stable collapse into a Big Bang curvature singularity. Under an additional condition on the first positive eigenvalue of $-Δ_γ$ satisfied, for example, by closed hyperbolic 3-manifolds of small diameter, we prove that the data evolves to a future complete spacetime in the expanding direction which asymptotes to a vacuum Friedman solution with $(M,γ)$ as the expansion normalized spatial geometry. In particular, the Strong Cosmic Censorship conjecture holds for this class of solutions in the $C^{2}$-sense. |
| title | Cosmic Censorship near FLRW spacetimes with negative spatial curvature |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs 83C75 (Primary), 35B35, 35Q76, 83C05, 83F05 (Secondary) |
| url | https://arxiv.org/abs/2211.08052 |