Nonstatic Schwarzschild model of a star

The relativistic Schwarzschild model of a static spherically symmetric star of uniform density is extended to the case in which the star is allowed to expand or contract. It is shown that the velocity of expansion or contraction of such a star obeys a law of the form $v=Hr$, where $r$ is the distance from the center. It is further shown that all homologous perturbations of such a star lead either to infinite expansion or to gravitational collapse.