Spherical gravitational collapse with tangential pressure

Abstract

We study the spherical gravitational collapse of a compact object under the approximation that the radial pressure is identically zero, and the tangential pressure is related to the density by a linear equation of state . It turns out that the Einstein equations 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 region near the centre which necessarily expands outwards, if collapse begins from rest. This region could be surrounded by an inward moving one which could collapse to a singularity - any such singularity will necessarily be spacelike. If this collapsing shell exists it might, in turn, be surrounded by a second expanding region. For negative k the entire object collapses inwards, but any singularities that could arise are not naked, except possibly at the centre. Thus the nature of the evolution is very different from that of dust, even when k is infinitesimally small. In the case of collapsing dust, there are certain initial configurations in which the collapse leads to the formation of a naked singularity.