Dynamics of geodesic motion in static cylindrically symmetric $\Lambda$-vacuum spacetimes

Abstract

We present a comparative study about the dynamics of geodesic orbits in static cylindrically symmetric vacuum spacetimes with and without a cosmological constant $\Lambda$. In particular, we analyse the orbital stability of the $\Lambda=0$ case with respect to the introduction of arbitrarily small values of $|\Lambda|$ and single out the cases where bounded orbits become unbounded.