Explicit isometric embeddings of collapsing dust ball

A. D. Kapustin, M. Ioffe, S. A. Paston

Результат исследований: Научные публикации в периодических изданияхстатья

Аннотация

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).

Язык оригиналаАнглийский
Номер статьи075019
Число страниц17
ЖурналClassical and Quantum Gravity
Том37
Номер выпуска7
Ранняя дата в режиме онлайн11 фев 2020
DOI
СостояниеОпубликовано - 9 апр 2020

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