Conformally flat sources for the Linet-Tian spacetime

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 $Λ\leq 0$ 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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