Complete solutions to the metric of spherically collapsing dust in an
  expanding spacetime with a cosmological constant
  We present semi-analytical solutions to the background equations describing
the Lema\^itre-Tolman-Bondi (LTB) metric as well as the homogeneous Friedmann
equations, in the presence of dust, curvature and a cosmological constant
Lambda. 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. Hence, these solutions
describe the complete space time of a collapsing spherical object in an
expanding universe. In the appendix we present for completeness a solution of
the Friedmann equations in the additional presence of radiation, only valid for
the Robertson-Walker metric.
