Matching the Linet-Tian spacetime with conformally flat cylindrically symmetric sources

Abstract

We consider static cylindrically symmetric spacetimes with a cosmological constant Lambda and obtain conformally flat solutions of the Einstein field equations. For these interior solutions we study the matching problem with the exterior Linet-Tian spacetime ([2],[3]), which is a generalization of the Levi-Civita spacetime including a cosmological constant, and show that the matching is possible if Lambda > 0. This work generalizes the results obtained in [1] for the Lambda = 0 case, where it was proved that static cylindrically symmetric sources matched to the Levi-Civita spacetime do not admit conformally flat solutions. The only known interiors to the Linet-Tian spacetime are the dust Einstein static spacetime [4] and static cylindrical shell sources [5].