  In this paper, we consider the problems of spherical gravitational collapse
and accretion using a spherically symmetric, spatially homothetic spacetime,
that is, as an exact solution (cqg1) of the field equations of general
relativity. Properties of matter like its equation of state determine whether
the collapse becomes unstoppable or not since the spacetime under consideration
admits any equation of state for matter in it. We can therefore describe the
formation of a semi-stable object here. {\bf A black hole may form in the
unstoppable gravitational collapse and/or accretion but only as an infinite
red-shift surface that is, however, not a null hyper-surface.} Therefore,
spherical, astrophysical black holes will always be of this type. This result
will have important implications for observational astrophysics and other
considerations in General Relativity based on the conception of black hole as a
null hyper-surface.
