  We study the geodesic motion in a space-time describing a swirling universe.
We show that the geodesic equations can be fully decoupled in the
Hamilton-Jacobi formalism leading to an additional constant of motion. The
analytical solutions to the geodesic equations can be given in terms of
elementary and elliptic functions. We also consider a space-time describing a
static black hole immersed in a swirling universe. In this case, full
separation of variables is not possible and the geodesic equations have to be
solved numerically.
