Variations on Birkhoff's theorem
  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.
