Geodesics dynamics in the Linet–Tian spacetime with $\Lambda <0$

Abstract

We investigate the geodesics' kinematics and dynamics in the Linet-Tian metric with $\Lambda<0$ and compare with the results for the Levi-Civita metric, when $\Lambda=0$. This is used to derive new stability results about the geodesics' dynamics in static vacuum cylindrically symmetric spacetimes with respect to the introduction of $\Lambda<0$.

In particular, we find that increasing $|\Lambda|$ always increases the minimum and maximum radial distances to the axis of any spatially confined planar null geodesic. Furthermore, we show that, in some cases, the inclusion of any $\Lambda<0$ breaks the geodesics' orbit confinement of the $\Lambda=0$ metric, for both planar and non-planar null geodesics, which are therefore unstable.

Using the full system of geodesics' equations, we provide numerical examples which illustrate our results.