Conformally flat sources for the Linet-Tian spacetime

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 $\Lambda \le 0$ 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.

Accepted for publication in General Relativity and Gravitation

References in corpus (5)

• Shearfree Cylindrical Gravitational Collapse
• Cylindrical spacetimes with a cosmological constant and their sources
• The Linet-Tian solution with a positive cosmological constant in four and higher dimensions
• Effect of a positive cosmological constant on cosmic strings
• First order perturbations of the Einstein-Straus and Oppenheimer-Snyder models

Cited by in corpus (3)

• Geodesics dynamics in the Linet-Tian spacetime with Lambda<0
• Geodesics dynamics in the Linet-Tian spacetime with Lambda>0
• Static Cylindrical Symmetric Solutions in the Einstein-Aether Theory