Static cylindrically symmetric gravitational field with cosmological constant

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

“…Circular geodesics for Λ < 0 were investigated in [2]. Interestingly, they found that σ determines whether the geodesics are timelike, null or spacelike, independently of their radial distance to the axis [2]. A similar property was already known for the LC spacetime for which, in the corresponding cases, σ is lower, equal or greater than 1/4.…”

“…Here, we extend the results of [2], giving a clearer view of the parameters involved by defining an appropriate effective potential and by analysing the dynamics of not only planar, but also non-planar geodesics. Also, differently from [2], in some occasions, we use a linear perturbative approach which allows us, in a mathematically more precise way, to study the effects on the orbits of the introduction of an arbitrarily small Λ.…”

“…which indicates that there are no trapped cylinders, in this case. However, as was pointed out in [2], there exist families of trapped null planar geodesics and we will explore those aspects in more detail ahead also generalising some of their results to the non-planar case.…”

“…Circular geodesics for Λ < 0 were investigated in [2]. Interestingly, they found that σ determines whether the geodesics are timelike, null or spacelike, independently of their radial distance to the axis [2].…”

“…However, little has been done about the stability of geodesics with respect to the introduction of a Λ term in the Einstein field equations. Banerjee et al [2] were the first to consider the study of geodesics in LT spacetimes by investigating the dynamics of planar geodesics in terms of the constant σ. In particular, they derived conditions under which null and timelike geodesics are confined or may escape to infinity.…”