A rotating cylinder in an asymptotically locally anti-de Sitter background

TL;DR

This paper presents exact solutions describing a rotating dust cylinder in an anti-de Sitter background, revealing conditions for closed timelike curves and asymptotic anti-de Sitter behavior.

Contribution

It introduces a new family of exact solutions for rotating cylinders in anti-de Sitter space, linking interior Godel solutions with exterior Linet-Tian solutions.

Findings

Exterior solutions depend on interior rotation and radius.

For certain parameters, the exterior resembles Linet-Tian solution.

Beyond a limit, the spacetime contains closed timelike curves.

Abstract

A family of exact solutions is presented which represents a rigidly rotating cylinder of dust in a background with a negative cosmological constant. The interior of the infinite cylinder is described by the Godel solution. An exact solution for the exterior solution is found which depends both on the rotation of the interior and on its radius. For values of these parameters less than a certain limit, the exterior solution is shown to be locally isomorphic to the Linet-Tian solution. For values larger than another limit, it is shown that the exterior solution extends into a region which contains closed timelike curves. At large distances from the source, the space-time is shown to be asymptotic locally to anti-de Sitter space.