SPHERICAL GRAVITATIONAL COLLAPSE WITH TANGENTIAL PRESSURE

We study the spherical gravitational collapse of a compact object unde r the approximation that the radial pressure is identically zero, and the tangential pressure ps is related to the density rho by a linear e quation of state p(theta) = k rho. It turns out that the Einstein equa tions can be reduced to the solution of an integral for the evolution of the area radius. We show that for positive k there is a finite regi on near the centre which necessarily expands outwards, if collapse beg ins from rest. This region could be surrounded by an inward moving one which could collapse to a singularity-any such singularity will neces sarily be spacelike. If this collapsing shell exists it might, in turn , be surrounded by a second expanding region. For negative k the entir e object collapses inwards, but any singularities that could arise are not naked, except possibly at the centre. Thus the nature of the evol ution is very different from that of dust, even when k is infinitesima lly small. In the case of collapsing dust, there are certain initial c onfigurations in which the collapse leads to the formation of a naked singularity.