Global analysis of the Kerr-Taub-NUT metric
Abstract
The Kerr-Taub-NUT metric is a local analytic solution of the vacuum Einstein-Maxwell equations. When the metric is expressed in Schwarzschild-like coordinates, two types of coordinate singularity are present. One occurs at certain values of the ``radial'' coordinate where grr becomes infinite and corresponds to bifurcate Killing horizons; the other occurs at θ=0,π, where the determinant of the components of the metric vanishes. It is shown that for nonzero NUT parameter the fixed points of the bifurcate Killing horizons and the degeneracies at θ=0,π cannot all be covered in one manifold. A maximal analytic manifold is constructed which covers the degeneracies at θ=0,π. It is non-Hausdorff but contains maximal Hausdorff subspaces, topologically S3×R, which reduce to Taub-NUT space for vanishing Kerr parameter. Kerr-Taub space can be interpreted as a closed, inhomogeneous electromagnetic-gravitational wave undergoing gravitational collapse. Another maximal analytic manifold is constructed which covers the fixed points of the bifurcate Killing horizons and the degeneracy at θ=0. It is suggested that this manifold represents the superposition of the Kerr geometry and a massless source of angular momentum at θ=π characterized by the NUT parameter.