  The gravitational collapse of a spherically symmetric massive core of a star
in which the fluid component is interacting with a growing vacuum energy
density filling a FLRW type geometry with an arbitrary curvature parameter is
investigated. The complete set of exact solutions for all values of the free
parameters are obtained and the influence of the curvature term on the
collapsing time, black hole mass and other physical quantities are also
discussed in detail. We show that for the same initial conditions the total
black hole mass depends only on the effective matter density parameter
(including the vacuum component). It is also shown that the analytical
condition to form a black hole i.e. the apparent horizon is not altered by the
contribution of the curvature terms, however, the remaining physical quantities
are quantitatively modified.
