# On the behavior of causal geodesics on a Kerr-de Sitter spacetime

## TL;DR

This paper investigates the behavior and completeness of causal geodesics in Kerr-de Sitter spacetime, revealing similarities with Kerr spacetime and highlighting the effects of ring singularities on geodesic paths.

## Contribution

It provides a comprehensive analysis of causal geodesics in Kerr-de Sitter spacetime, establishing their completeness properties and the influence of ring singularities.

## Key findings

- Causal geodesics avoiding the ring singularity are complete.
- Geodesics hitting the ring singularity are primarily equatorial.
- The ring singularity exhibits a repulsive effect on geodesics.

## Abstract

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 (IVP) whose solutions lead to a global understanding of causal geodesics on these spacetime. Causal geodesics that avoid the rotation axis are complete except the ones that hit the ring-like 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.