Variations on Birkhoff's theorem

Understand

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.