Geodesics dynamics in the Linet–Tian spacetime with Λ > 0

Abstract

We analyse the geodesics' dynamics in cylindrically symmetric vacuum spacetimes with $\Lambda>0$ and compare it to the $\Lambda= 0$ and $\Lambda<0$ cases. When $\Lambda>0$ there are two singularities in the metric which brings new qualitative features to the dynamics. We find that $\Lambda=0$ planar timelike confined geodesics are unstable against the introduction of a sufficiently large $\Lambda$, in the sense that the bounded orbits become unbounded. In turn, any non-planar radially bounded geodesics are stable for any positive $\Lambda$. We construct global non-singular static vacuum spacetimes in cylindrical symmetry with $\Lambda>0$ by matching the Linet-Tian metric with two appropriate sources.