Explicit isometric embeddings of collapsing dust ball
| Autor: | Kapustin, A. D., Ioffe, M. V., Paston, S. A. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Class. Quantum Grav. 37 (2020) 075019 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1361-6382/ab74f8 |
| Popis: | 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). Comment: LaTeX, 18 pages |
| Databáze: | arXiv |
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