论文标题
重力浪潮宇宙学的空间奇异性的定量爆炸估计值
Quantitative blow-up estimates for spacelike singularities in gravitational-collapse cosmological spacetimes
论文作者
论文摘要
在球形对称性下，带有双空坐标$（U，V）$，我们研究了Einstein的重力崩溃 - 量表现场系统，具有正宇宙常数。当区域半径$ r $消失并且具有空间时，时空奇点就会出现。我们得出了新的定量估计，以获取各种数量的多项式爆炸率$ O（1/r^n）$，并将第一作者和张的结果扩展到[5]中，以及第一作者和Gajic在[3]中的论点，并将其扩展到宇宙设置。特别是，我们在[5]中提高了$ r \ partial_u r $和$ r \ r \ partial_v r $的估计，并证明了$ r（u，v）= 0 $的空间般的奇异性是$ c^{1,1/3} $ in $（u（u，v）$ coordinates $ coordinates。作为一种应用，这些估计值还为Einstein-Euler系统的硬相模型的流体速度和密度的上限提供了定量的爆破上限。在及时的无限段附近，我们还通过将Kretschmann标量的精确爆炸率与事件范围内指数价格定律联系起来，从而在[3]中概括了定理。在宇宙学的环境中，这进一步揭示了首次沿空间度奇异性的质量流动现象。
Under spherical symmetry, with double-null coordinates $(u,v)$, we study the gravitational collapse of the Einstein--scalar field system with a positive cosmological constant. The spacetime singularities arise when area radius $r$ vanishes and they are spacelike. We derive new quantitative estimates, obtain polynomial blow-up rates $O(1/r^N)$ for various quantities, and extend the results in [5] by the first author and Zhang and the arguments in [3] by the first author and Gajic to the cosmological settings. In particular, we sharpen the estimates of $r\partial_u r$ and $r\partial_v r$ in [5] and prove that the spacelike singularities where $r(u,v)=0$ are $C^{1,1/3}$ in $(u,v)$ coordinates. As an application, these estimates also give quantitative blow-up upper bounds of fluid velocity and density for the hard-phase model of the Einstein-Euler system under irrotational assumption. Near the timelike infinity, we also generalize the theorems in [3] by linking the precise blow-up rates of the Kretschmann scalar to the exponential Price's law along the event horizon. In cosmological settings, this further reveals the mass-inflation phenomena along the spacelike singularities for the first time.
