Maximal Analytic Extension of the Kerr Metric
Abstract
Kruskal's transformation of the Schwarzschild metric is generalized to apply to the stationary, axially symmetric vacuum solution of Kerr, and is used to construct a maximal analytic extension of the latter. In the low angular momentum case, a^{2} < m^{2}, this extension consists of an infinite sequence EinsteinRosen bridges joined in time by successive pairs of horizons. The number of distinct asymptotically flat sheets in the extended space can be reduced to four by making suitable identifications. Several properties of the Kerr metric, including the behavior of geodesics lying in the equatorial plane, are examined in some detail. Completeness is demonstrated explicitly for a special class of geodesics, and inferred for all those that do not strike the ring singularity.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 February 1967
 DOI:
 10.1063/1.1705193
 Bibcode:
 1967JMP.....8..265B