General geodesic motion in the extended Kerr manifold

The timelike and null geodesics in the Kerr metric describe important properties of the space surrounding a rotating black hole. The general characteristics of these geodesics, with an emphasis on those on the axis of symmetry and the equatorial plane, are found. On the axis of symmetry, the behavior of all timelike and null geodesics is completely described. The accessibility of various spaces added for geodesic completeness in the extended manifold is found by making local observations of geodesics in one coordinate patch from geodesics in another. The analysis on the equatorial plane shows that for a given angular momentum, P/sub phi/, if the energy, -P/sub t/, is in the range aP/sub phi//2mr/sub +/ less than -P/sub t/ less than aP/sub phi//2mr/sub -/, the geodesic, for r greater than r/sub +/, is in the I region and, for r less than r/sub -/, is in the III' region in Carter's version of the extended manifold. The energy and momentum of circular orbits, as functions of r and a, in the equatorial plane are found. The limits of the motion in the theta direction are found explicitly as functions of the constants of the motion. This analysis shows that there is geodesic motion on the equatorial plane that is unstable in the theta direction. This instability is most pronounced for all zero angular momentum unbound orbits; in this case, there is no minimum or maximum theta, and any perturbation could carry the geodesic to the axis of symmetry. Lastly, to show the nature of a surface containing theta geodesics, Carter's null surface is imbedded in a three dimensional Minkowski space. (Diss. Abstr. Int., B)