Viscous fluid collapse

The problem of seeking solutions of Einstein's field equations that represent the collapse of realistic matter distributions is discussed. A specialized approach to this problem is taken in which the fact that a given energy-momentum tensor may formally represent different types of matter distribution is exploited. A solution is presented in which an "interior" solution consisting of a collapsing viscous fluid (i.e., a solution of the Einstein field equations for an imperfect fluid source) is matched continuously across its boundary to a Schwarzschild "exterior." In this solution the geometrical part corresponding to the interior solution is formally identical to that of a closed (i.e., $k=+1\mathrm{}$) Friedmann-Robertson-Walker dust model.