THE KERR SPACE-TIME NEAR THE RING SINGULARITY

We investigate the geometry of the Kerr space-time near the ring singularity. A systematic study of the mathematical and physical structure of this region reveals that the singularity in the Kerr space-time is naturally understood in terms of a subset of the immersion of the set defined by r=0 (in Boyer-Lindquist coordinates) in the Kerr space-time. It is well known that the Kerr space-time is not a differentiable manifold (due to the curvature singularity) or a topological manifold, but a well defined topological space with a structure that is manifested by the constrast in taking limits along the hypersurface at r=0 and the equatorial plane which approach singularity. We find that the ring singularity is either an edge or a self-intersection of the topological space depending on which extension of the metric through r=0 is implemented. A major result of this analysis is the extrapolation to the general accelerating case of Carter's proof that the only nonspacelike geodesics which can reach the ring singularity are restricted to the equatorial plane. For finite magnitudes of proper acceleration, it is shown that only lightlike trajectories that asymptotically approach the null generator of the ring singularity can reach it from above or below the equatorial plane. © 1990 Plenum Publishing Corporation.