We investigate the matching, across cylindrical surfaces, of static cylindrically symmetric conformally flat spacetimes with a cosmological constant Λ, satisfying regularity conditions at the axis, to an exterior Linet-Tian spacetime. We prove that for Λ ≤ 0 such matching is impossible. On the other hand, we show through simple examples that the matching is possible for Λ > 0. We suggest a physical argument that might explain these results. *
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