General geodesic motion in the extended Kerr manifold
Abstract
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 presented. 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. 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.
 Publication:

Ph.D. Thesis
 Pub Date:
 1974
 Bibcode:
 1974PhDT........11S
 Keywords:

 Angular Momentum;
 Black Holes (Astronomy);
 Celestial Geodesy;
 Kerr Effects;
 Equatorial Orbits;
 Geodetic Coordinates;
 Manifolds (Mathematics);
 Minkowski Space;
 Astrophysics