Slowly rotating perfect fluids with a cosmological constant

TL;DR

This paper extends Hartle's slow rotation formalism to include a cosmological constant, deriving a generalized metric and demonstrating that the Wahlquist solution can model isolated rotating bodies in an (anti)-de Sitter universe.

Contribution

It develops a generalized Hartle-Thorne metric with a cosmological constant and shows Wahlquist's solution can represent isolated rotating bodies in such spacetimes.

Findings

Derived the Hartle-Thorne-(anti)-de Sitter metric.

Wahlquist's solution can be matched to asymptotic (anti)-de Sitter space.

Established a model for isolated rotating bodies with a cosmological constant.

Abstract

Hartle's slow rotation formalism is developed in the presence of a cosmological constant. We find the generalisation of the Hartle-Thorne vacuum metric, the Hartle-Thorne-(anti)-de Sitter metric, and find that it is always asymptotically (anti)-de Sitter. Next we consider Wahlquist's rotating perfect fluid interior solution in Hartle's formalism and discuss its matching to the Hartle-Thorne-(anti)-de Sitter metric. It is known that the Wahlquist solution cannot be matched to an asymptotically flat region and therefore does not provide a model of an isolated rotating body in this context. However, in the presence of a cosmological term, we find that it can be matched to an asymptotic (anti)-de Sitter space and we are able to interpret the Wahlquist solution as a model of an isolated rotating body, to second order in the angular velocity.