Complete Analytic Extension of the Symmetry Axis of Kerr's Solution of Einstein's Equations

Phys. Rev. 141, 1242 – Published 28 January 1966
Brandon Carter


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 a2<~m2. The method developed by Kruskal for completing the Schwarzschild solution is adapted to the distinct cases a2<m2 and a2=m2. 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

Authors & Affiliations

Brandon Carter

  • Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England

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