Conformally flat sources for the Linet-Tian spacetime

TL;DR

This paper examines the conditions under which static cylindrically symmetric conformally flat spacetimes can be matched to Linet-Tian spacetimes, revealing that such matching is only possible for positive cosmological constant values.

Contribution

It demonstrates the impossibility of matching for non-positive cosmological constants and provides examples and physical reasoning for the case when the cosmological constant is positive.

Findings

Matching impossible for Λ ≤ 0

Matching possible for Λ > 0

Physical argument explaining the results

Abstract

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.