球对称时空中的环猜想
The Hoop Conjecture in Spherically Symmetric Spacetimes
摘要：
在满足主能量条件的球对称初始数据集上，给出了由于物质集中而导致的俘获面存在的一般性充分条件。这些结果是新颖的，因为它们适用于任意类空切片，是有意义的，也就是说，他们不需要任何辅助假设，如极大值，时间对称性，或特殊的外在叶理，最重要的是，他们可以很容易地推广到非球形的情况下，一旦一个存在理论的一个修改版本的张方程的发展。此外，我们的方法也产生积极性和单调性的Misner-Sharp能量。
英文摘要：
We give general sufficient conditions for the existence of trapped surfaces due to concentration of matter in spherically symmetric initial data sets satisfying the dominant energy condition. These results are novel in that they apply and are meaningful for arbitrary spacelike slices, that is they do not require any auxiliary assumptions such as maximality, time-symmetry, or special extrinsic foliations, and most importantly they can easily be generalized to the nonspherical case once an existence theory for a modified version of the Jang equation is developed. Moreover, our methods also yield positivity and monotonicity properties of the Misner-Sharp energy.
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