On the formation of trapped surfaces
On the formation of trapped surfaces
复制标题
DOI：
10.1007/978-3-642-25361-4_10
复制
发表时间：
2009-12
期刊：
影响因子：
3.7
通讯作者：
S. Klainerman;I. Rodnianski
中科院分区：
文献类型：
--
作者：
S. Klainerman;I. Rodnianski
在最近的一项重大突破D. Christodoulou解决了一个长期存在的问题，广义相对论的演化形成的囚禁面在爱因斯坦真空时空。他已经确定了一个开放的一组经常性的初始条件在一个传出的零超曲面（有限的和在过去的零无限）导致形成一个被困的表面在相应的真空时空的未来的初始传出超曲面和另一个传入的零超曲面与规定的闵可夫斯基数据。在本文中，我们给出了一个更简单的证明有限的问题，通过扩大可接受的初始条件，并与此一致，放松相应的传播估计只是足够的一个陷阱表面仍然形成。我们还减少了在参数中所需的导数的数量从两个导数的曲率只有一个。更重要的是，证明，这可以很容易地本地化相对于角扇区，有进一步发展的潜力。
In a recent important breakthrough D. Christodoulou has solved a long standing problem of General Relativity of evolutionary formation of trapped surfaces in the Einstein-vacuum space-times. He has identified an open set of regular initial conditions on an outgoing null hypersurface (both finite and at past null infinity) leading to a formation a trapped surface in the corresponding vacuum space-time to the future of the initial outgoing hypersurface and another incoming null hypersurface with the prescribed Minkowskian data. In this paper we give a simpler proof for a finite problem by enlarging the admissible set of initial conditions and, consistent with this, relaxing the corresponding propagation estimates just enough that a trapped surface still forms. We also reduce the number of derivatives needed in the argument from two derivatives of the curvature to just one. More importantly, the proof, which can be easily localized with respect to angular sectors, has the potential for further developments.