Black Hole Formation with an Interacting Vacuum Energy Density: Curvature Effects

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.