The Gravitational Collapse of a Slowly Rotating Relativistic Star

Abstract

A discussion is presented of the coupling between the angular momentum of a collapsing star and the gravitational field. A rotational perturbation is applied to a spherically symmetric, time-dependent interior solution of the Einstein field equations. Equations are derived for the perturbed metric component h 03, which demonstrate the effects of the collapse, and solutions are given to order c–5 . An application of these results to the general relativistic law of conservation of total angular momentum indicates that appreciable Newtonian angular momentum may be dissipated during the final stages of gravitational collapse. Post-Newtonian terms in the angular momentum, together with estimates of the time scale for this effect, are given for a sequence of polytropic stellar models. It is also found that the effect of general relativity is to increase the angular momentum above its Newtonian value for a uniformly rotating star of low eccentricity and of given equatorial radius, this effect increasing with central condensation of the star.