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 $\Lambda$, satisfying regularity conditions at the axis, to an exterior Linet-Tian spacetime. We prove that for $\Lambda\leq 0$ such matching is impossible. On the other hand, we show through simple examples that the matching is possible for $\Lambda>0$. We suggest a physical argument that might explain these results. 
Irene Brito, M. F. A. da Silva, Filipe C. Mena, N. O. Santos
gr-qc