Local observations of geodesics in the extended Kerr manifold

Geodesics along the axis of symmetry in Carter's extension of the Kerr metric are divided into two types by the sign of the constant of the motion associated with the timelike Killing vector, and it is shown that this also divides them as to their place of origin on the manifold, which contains infinitely many copies of two different spaces which are flat at r = ± ∞. It is shown that geodesics cannot cross from one space to the other, but that a trajectory with properly applied acceleration can cross over.