A complete analytic extension of the Kerr metric along the symmetry axis is obtained by expanding the method developed by Kruskal for extending the Schwarzschild metric. It is found that only two co-ordinate patches are required for the complete analytic extension. Upon investigating geodesic trajectories in the Kerr field it is found that the phenomenon of self-intersecting world lines can occur. The effect is compared with similar self-collisions that may occur in a Schwarzschild field.
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