标题： 带有$Λ<0$的再坍缩时空 显示英文标题

标题： Recollapsing spacetimes with $Λ<0$

摘要： 我们证明，任何具有 $\Lambda<0$ 的齐次初始数据集，在正交形式为 $(F\times \mathbb S^1,a_0^2dz^2+b_0^2\sigma^2,c_0dz^2+d_0\sigma)$ 的乘积3流形上，其中 $(F,\sigma)$ 是常曲率的闭合2曲面， $a_0,..., d_0$ 是合适的常数，会在带有负宇宙常数的爱因斯坦流下重新坍缩，并在大爆炸和大挤压处形成紧缩奇点。 在这些奇点中，Kretschmann标量保持有界，因此这些不是曲率奇点。 然后我们证明，无质量标量场的存在会导致对应类中的所有解在时空两端的Kretschmann标量发散。 通过标准论证，这种重新坍缩行为会扩展到初始数据集的一个开邻域，并且在接近齐次区域时在这种意义上是普遍的。 显示英文摘要

摘要： We show that any homogeneous initial data set with $\Lambda<0$ on a product 3-manifold of the orthogonal form $(F\times \mathbb S^1,a_0^2dz^2+b_0^2\sigma^2,c_0dz^2+d_0\sigma)$, where $(F,\sigma)$ is a closed 2-surface of constant curvature and $a_0,..., d_0$ are suitable constants, recollapses under the Einstein-flow with a negative cosmological constant and forms crushing singularities at the big bang and the big crunch, respectively. Towards certain singularities among those the Kretschmann scalar remains bounded, hence these are not curvature singularities. We then show that the presence of a massless scalar field causes the Kretschmann scalar to blow-up towards both ends of spacetime for all solutions in the corresponding class. By standard arguments this recollapsing behaviour extends to an open neighborhood in the set of initial data sets and is in this sense generic close to the homogeneous regime.