Behavior of causal geodesics on a Kerr-de Sitter spacetime

We analyze the behavior of causal geodesics on a Kerr-de Sitter spacetime with particular emphasis on their completeness property. We set up an initial value problem of which the solutions lead to a global understanding of causal geodesics on these spacetimes. Causal geodesics that avoid the rotation axis are complete except the ones that hit the ringlike curvature singularity and those that encounter the ring singularity are necessary equatorial ones. We also show the existence of geodesics that cross or lie on the rotation axis. The equations governing the latter family show the repulsive nature of the ring singularity. The results of this work show that, as far as properties of causal geodesics are concerned, Kerr-de Sitter spacetimes behave in a similar manner as the family of Kerr spacetimes.