论文标题
塌陷尘埃的显式等距嵌入
Explicit isometric embeddings of collapsing dust ball
论文作者
论文摘要
这项工作致力于搜索与黑洞形成的球形对称物质崩溃相对应的度量的显式等距嵌入。考虑了两种方法：首先，嵌入是为整个歧管构造的；在第二个中，使用了在尘埃球内外分别获得的解决方案的想法。在第一种方法的框架中，构建了具有签名（2 + 5）的7D空间中的全局平滑嵌入。它对应于从无穷大落下的物质导致的地平线形成。第二种方法通常会导致具有签名（1 + 6）的7D空间中的嵌入。这种嵌入对应于物质从白孔中飞出而随着其地平线消失而飞出的情况，然后尘埃球的半径达到最大值，然后随着黑洞的地平线形成而发生崩溃。所获得的嵌入到处都不是光滑的 - 它在防尘球的边缘包含一个扭结，{另外，它}并不完全全球。在特定情况下，当尘埃球的最大半径与地平线半径重合时，可以在具有签名的平坦6D空间中构造全局平滑嵌入（1 + 5）。
The work is devoted to the search for explicit isometric embeddings of a metric corresponding to the collapse of spherically symmetric matter with the formation of a black hole. Two approaches are considered: in the first, the embedding is constructed for the whole manifold at once; in the second, the idea of a junction of solutions, obtained separately for areas inside and outside the dust ball, is used. In the framework of the first approach, a global smooth embedding in 7D space with a signature (2 + 5) was constructed. It corresponds to the formation of the horizon as a result of matter falling from infinity. The second approach generally leads to an embedding in 7D space with the signature (1 + 6). This embedding corresponds to the case when matter flies out of a white hole with the disappearance of its horizon, after which the radius of the dust ball reaches its maximum, and then a collapse occurs with the formation of the horizon of a black hole. The embedding obtained is not smooth everywhere --- it contains a kink on the edge of the dust ball, and {also, it is} not quite global. In the particular case, when the maximum radius of the dust ball coincides with the radius of the horizon, it is possible to construct a global smooth embedding in a flat 6D space with a signature (1 + 5).
