Complete solutions to the metric of spherically collapsing dust in an expanding spacetime with a cosmological constant

We present elliptic solutions to the background equations describing the LemaItre-Tolman-Bondi metric as well as the homogeneous Friedmann equation, in the presence of dust, curvature and a cosmological constant I >. For none of the presented solutions any numerical integration has to be performed. All presented solutions are given for expanding and collapsing phases, preserving continuity in time and radius; both radial and angular scale functions are given. Hence, these solutions describe the complete spacetime of a collapsing spherical object in an expanding universe, as well as those of ever expanding objects. In the appendix we present for completeness a solution of the Friedmann equation in the additional presence of radiation, only valid for the Robertson-Walker metric.