Slowly rotating voids in cosmology

TL;DR

This paper models a slowly rotating void in a cosmological setting, analyzing frame dragging and star motion to explore Machian effects in a universe with a rotating shell separating an empty void from a FLRW dust universe.

Contribution

It introduces a unified perturbative approach to study slow rotation effects in a void embedded in various FLRW cosmologies, including frame dragging and Machian phenomena.

Findings

Derived expressions for inertial frame dragging due to the rotating shell.

Analyzed apparent star motions within the void caused by rotation.

Discussed measurable Machian effects in the cosmological context.

Abstract

We consider a spacetime consisting of an empty void separated from an almost Friedmann-Lema\^\i tre-Robertson-Walker (FLRW) dust universe by a spherically symmetric, slowly rotating shell which is comoving with the cosmic dust. We treat in a unified manner all types of the FLRW universes. The metric is expressed in terms of a constant characterizing the angular momentum of the shell, and parametrized by the comoving radius of the shell. Treating the rotation as a first order perturbation, we compute the dragging of inertial frames as well as the apparent motion of distant stars within the void. Finally, we discuss, in terms of in principle measurable quantities, 'Machian' features of the model.