  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).
