TY - JOUR

T1 - Explicit isometric embeddings of collapsing dust ball

AU - Kapustin, A. D.

AU - Ioffe, M.

AU - Paston, S. A.

PY - 2020/4/9

Y1 - 2020/4/9

N2 - 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).

AB - 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).

KW - isometric embedding

KW - gravitational collapse

KW - black holes

KW - FLAT SPACE

KW - GRAVITY

KW - FIELD

UR - http://www.scopus.com/inward/record.url?scp=85082428595&partnerID=8YFLogxK

U2 - 10.1088/1361-6382/ab74f8

DO - 10.1088/1361-6382/ab74f8

M3 - статья

VL - 37

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 7

M1 - 075019

ER -