On the end stage of spherical gravitational collapse in a cosmological scenario
We consider the end stage of spherical gravitational collapse in a cosmological setting. As an alternative to standard spherical top hat collapse, an expanding FLRW metric is matched to a generic contracting solution of Einstein's equations on a space like hypersurface. Using the Israel junction conditions, this is done at a time when the scale factor of expansion reaches its maximum value. In this scenario, we first show that inhomogeneous dust collapse of the LTB type are ruled out by virtue of the junction conditions. We then investigate non dust like collapse with vanishing radial pressure, and show that this can lead to a known regular interior Schwarzschild solution, without ad hoc virialization. The other possibilities at equilibrium invariably lead to naked singularities, and we obtain a new class of such naked singularities. Finally, we consider a simplistic analytic model for collapse, and show via the matching process that it can lead to the formation of singularity free space times as the end stage, while respecting the known cosmological parameters. The presence of trapped surfaces in this example do not lead to singularities, due to a violation of the strong energy condition.