The Linet-Tian solution with a positive cosmological constant in four and higher dimensions

Abstract

The static, apparently cylindrically symmetric vacuum solution of Linet and Tian for the case of a positive cosmological constant $\Lambda$ is shown to have toroidal symmetry and, besides $\Lambda$, to include three arbitrary parameters. It possesses two curvature singularities, of which one can be removed by matching it across a toroidal surface to a corresponding region of the dust-filled Einstein static universe. In four dimensions, this clarifies the geometrical properties, the coordinate ranges and the meaning of the parameters in this solution. Some other properties and limiting cases of this space-time are described. Its generalisation to any higher number of dimensions is also explicitly given.

6 pages, 1 figure. To appear in Phys. Rev. D

References in corpus (8)

• The AdS/CFT Correspondence and a New Positive Energy Conjecture for General Relativity
• Strings in de Sitter space
• On the Levi-Civita solutions with cosmological constant
• Cylindrical spacetimes with a cosmological constant and their sources
• Gravitational waves propagating into Friedmann--Robertson--Walker universes
• Effect of a positive cosmological constant on cosmic strings
• A note on cosmological Levi-Civita spacetimes in higher dimensions
• Comment on the new AdS universe

Cited by in corpus (16)

• Cylindrical Systems in General Relativity
• Interpreting spacetimes of any dimension using geodesic deviation
• Asymptotically anti-de Sitter cylindrical thin-shell wormholes
• Cylindrically symmetric static solutions of the Einstein field equations for elastic matter
• Geodesics dynamics in the Linet-Tian spacetime with Lambda<0
• Conformally flat sources for the Linet-Tian spacetime
• Dark fluid or cosmological constant : Why there are different de Sitter-type spacetimes
• Non-expanding Plebanski-Demianski space-times
• Geodesics dynamics in the Linet-Tian spacetime with Lambda>0
• Translation in Cylindrically Symmetric Vacuum
• Static Cylindrical Symmetric Solutions in the Einstein-Aether Theory
• Static and stationary dark fluid universes: A gravitoelectromagnetic perspective
• Interpreting A and B-metrics with $\Lambda$ as gravitational field of a tachyon in (anti-)de Sitter universe
• Linear stability of the Linet - Tian solution with negative cosmological constant
• Geodesic structure of the cosmological Levi-Civita spacetimes
• Cylindrically and toroidally symmetric solutions with a cosmological constant