Geodesics dynamics in the Linet-Tian spacetime with Lambda<0
  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. 
Irene Brito, M. F. A. da Silva, Filipe C. Mena and N. O. Santos
gr-qc