标题： 时空不可延展性准则通过体积-距离比渐近行为及其在裸奇点和FLRW时空中的应用 显示英文标题

标题： Spacetime inextensibility criteria by volume-distance-ratio asymptote and applications to naked singularities and FLRW spacetimes

摘要： 我们研究未来边界点处时空的不可延拓性问题。 我们通过类时菱形接近未来边界点时的体积-距离比渐进行为来检测时空的不可延拓性。 基本思想是将该渐进行为与闵可夫斯基时空中的相应行为进行比较。 通过这一思想，我们建立了$C^{0,1}$和$C^0$正则性的不可延拓性准则。 作为应用，我们证明了i) 在无质量标量场引力塌缩中由Christodoulou构造的球对称自相似裸奇点内部解的$C^{0,1}$不可延拓性。 关键估计是对裸奇点内部解在自相似坐标系中的体积形式的估计。 ii) 具有渐近线性尺度因子$a(t) \sim |t|$的空间平坦FLRW时空的$C^0$不可延拓性。 关键估计是与具有尺度因子$|t|$的空间双曲FLRW时空的体积比较，该尺度因子是闵可夫斯基时空中某一点的因果过去。 显示英文摘要

摘要： We study the inextensibility problem of the spacetime at a future boundary point. We detect the inextensibility of the spacetime by the volume-distance-ratio asymptote of the timelike diamond approaching the future boundary point. The fundamental idea is to compare the asymptote with the one in Minkowski spacetime. By this idea, we establish the inextensibility criteria for both $C^{0,1}$ and $C^0$ regularities. As applications, we prove that i) $C^{0,1}$-inextensibility of the interior solution of the spherically self-similar naked singularity in the gravitational collapse of a massless scalar field constructed by Christodoulou. The key estimate is on the volume form of the interior solution of the naked singularity in a self-similar coordinate system. ii) $C^0$-inextensibility of the spatially flat FLRW spacetime with asymptotically linear scale factor $a(t) \sim |t|$. The key estimate is the volume comparison with the spatially hyperbolic FLRW spacetime with the scale factor $|t|$ which is the causal past of a point in the Minkowski spacetime.