论文标题
FLRW空间近距离的宇宙审查制度为负空间曲率
Cosmic Censorship near FLRW spacetimes with negative spatial curvature
论文作者
论文摘要
我们考虑在封闭的$ 3 $ - manifold $（m，γ）上的爱因斯坦标量场系统的一般初始数据，该数据与Friedman-Lema-Robertson-Walker解决方案的数据接近，带有同质标量的田地物质，而Einstein Metric $γ$作为空间始发。我们证明，在爱因斯坦标量场系统中，这种初始数据的最大全球双曲线发育在收缩方向上已经不完整，并且表现出稳定的崩溃，成为大爆炸曲率的奇异性。 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.特别是，强大的宇宙审查猜想在$ c^{2} $ - sense中为此类别的解决方案保留。
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.
