Axially symmetric equilibrium regions of Friedmann-Lemaitre-Robertson-Walker universes

TL;DR

This paper proves that stationary, axisymmetric regions in FLRW universes must be static and spherically symmetric, confirming the uniqueness of the Einstein-Straus model and its limitations in explaining local physics within cosmic expansion.

Contribution

It establishes a new uniqueness theorem showing that only static, spherically symmetric vacuum regions can be matched to FLRW universes under axial symmetry.

Findings

Any orthogonally transitive stationary and axisymmetric region in FLRW must be static.

The only vacuum region compatible with FLRW under these conditions is Schwarzschild.

Supports the Einstein-Straus model's limitations in cosmological local physics.

Abstract

The study of the matching of stationary and axisymmetric spacetimes with Friedmann-Lemaitre-Robertson-Walker spacetimes preserving the axial symmetry is presented. We show, in particular, that any orthogonally transitive stationary and axisymmetric region in FLRW must be static, irrespective of the matter content. Therefore, previous results on static regions in FLRW cosmologies apply. As a result, the only stationary and axisymmetric vacuum region that can be matched to a (non-static) FLRW spacetime is a spherically symmetric region of Schwarzschild. This constitutes another uniqueness result for the Einstein-Straus model (as well as its Oppenheimer-Snyder counterpart), and hence another indication of its unsuitability as an answer to the influence of the cosmic expansion on local physics.