Does Birkhoff's theorem work just as well in the non-geometric approach to general relativity?
My guess is, that it should due to the equivalence with the geometric approach. On the other hand, gravity is now described by a (tensor) potential.
So, how does it avoid similar issues with boundary conditions, such as the shell theorem in Newtonian gravity can run into, such as in the question below?
Ambiguity in applying Newton's shell theorem in an infinite homogeneous universe
