论文标题
在低规度边界下被捕获的表面不存在
On the non-existence of trapped surfaces under low-regularity bounds
论文作者
论文摘要
在爱因斯坦磁场方程的溶液中，被困的表面的出现与低规律性方案中相应的库奇问题的拟态性特性密切相关。在本文中，当假定Cauchy数据的尺度不变大小时，我们研究了已经在初始超表面水平上的被困表面存在的问题。我们的主要定理指出，当Cauchy数据接近Minkowski时空（不一定是平面超平面）在BESOV $ B^{3/2} _ {2,1} $ NORAD上诱导的数据时，最初不存在被困的表面。我们还讨论了将上述结果扩展到仅假定$ h^{3/2} $的情况的问题。
The emergence of trapped surfaces in solutions to the Einstein field equations is intimately tied to the well-posedness properties of the corresponding Cauchy problem in the low regularity regime. In this paper, we study the question of existence of trapped surfaces already at the level of the initial hypersurface when the scale invariant size of the Cauchy data is assumed to be bounded. Our main theorem states that no trapped surfaces can exist initially when the Cauchy data are close to the data induced on a spacelike hypersurface of Minkowski spacetime (not necessarily a flat hyperplane) in the Besov $B^{3/2}_{2,1}$ norm. We also discuss the question of extending the above result to the case when merely smallness in $H^{3/2}$ is assumed.
