The 2-dimensional metric on the symmetry axis of the Kerr solution is examined and it is shown that in the form usually given it is incomplete when . The method developed by Kruskal for completing the Schwarzschild solution is adapted to the distinct cases and . In each case a singularity-free metric is obtained which is periodic with respect to a timelike coordinate, and which is shown to be a complete analytic extension. The generalization to the full 4-dimensional Kerr solution is discussed, and finally the questions of uniqueness and causality are considered.
- Received 25 June 1965
- Published in the issue dated January 1966
© 1966 The American Physical Society