Variations on Birkhoff's theorem

TL;DR

This paper explores generalizations of Birkhoff's theorem to include matter, perturbations, and geometric variations, examining implications for local vacuum solutions and the influence of dark matter on the solar system.

Contribution

It introduces new generalizations of Birkhoff's theorem considering matter, geometric variations, and perturbations, enhancing understanding of local vacuum solutions.

Findings

Dark matter's potential influence on the solar system is significant.

Generalizations of Birkhoff's theorem accommodate matter and perturbations.

Implications for the relation between cosmic expansion and local systems are discussed.

Abstract

The relation between the expanding universe and local vacuum solutions, such as that for the Solar System, is crucially mediated by Birkhoff's theorem. Here we consider how that relation works, and give generalizations of Birkhoff's theorem when there are geometric and matter and perturbations. The issue of to what degree dark matter might influence the solar system emerges as a significant question.