Geodesics dynamics in the Linet-Tian spacetime with Lambda>0

TL;DR

This paper investigates how positive cosmological constant Lambda influences geodesic behavior in cylindrically symmetric vacuum spacetimes, revealing new qualitative features and stability properties compared to Lambda=0 and Lambda<0 cases.

Contribution

It provides a detailed analysis of geodesic dynamics in Linet-Tian spacetime with Lambda>0 and constructs global non-singular solutions by matching with sources.

Findings

Planar timelike geodesics become unbounded with large Lambda.

Non-planar radially bounded geodesics remain stable for all positive Lambda.

New singularities and stability properties are identified in the Lambda>0 case.

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.