标题： 对带有碰撞无关物质的表面对称宇宙时空的强宇宙审查猜想 显示英文标题

标题： Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter

摘要： 本文讨论了包含自引力无碰撞物质的时空中的强宇宙审查猜想，这些时空从表面对称的紧致初始数据演化而来。 全局动力学表现出定性不同的特征，这取决于对称曲面的曲率$k$的符号和宇宙学常数$\Lambda$。 在合适的表述下，如果$\Lambda=0$或$k\le0$，$\Lambda>0$，则强宇宙审查猜想的问题得到肯定解决。 在情况$\Lambda>0$，$k=1$中，我们给出了时空可能的“边界”部分的详细几何特征；在这种情况下，显示强宇宙审查猜想的剩余障碍与极端施瓦茨希尔德-德西特型黑洞的可能形成有关。 在初始对称曲面均为扩张的特殊情况下，对于所有$k,\Lambda$，在过去方向上证明了强宇宙监督猜想。最后，我们的结果还导致了渐近平坦数据坍缩时黑洞内部未来的边界几何特征化：特别是，在施瓦茨希尔德数据的小扰动情况下，证明了这些解不表现出从$i^+$发出且具有严格正极限面积半径的柯西视界。 显示英文摘要

摘要： This paper addresses strong cosmic censorship for spacetimes with self-gravitating collisionless matter, evolving from surface-symmetric compact initial data. The global dynamics exhibit qualitatively different features according to the sign of the curvature $k$ of the symmetric surfaces and the cosmological constant $\Lambda$. With a suitable formulation, the question of strong cosmic censorship is settled in the affirmative if $\Lambda=0$ or $k\le0$, $\Lambda>0$. In the case $\Lambda>0$, $k=1$, we give a detailed geometric characterization of possible "boundary" components of spacetime; the remaining obstruction to showing strong cosmic censorship in this case has to do with the possible formation of extremal Schwarzschild-de Sitter-type black holes. In the special case that the initial symmetric surfaces are all expanding, strong cosmic censorship is shown in the past for all $k,\Lambda$. Finally, our results also lead to a geometric characterization of the future boundary of black hole interiors for the collapse of asymptotically flat data: in particular, in the case of small perturbations of Schwarzschild data, it is shown that these solutions do not exhibit Cauchy horizons emanating from $i^+$ with strictly positive limiting area radius.