Birkhoffs theorem in conformal gravity

It is pointed out that conformal gravity, derived from the action quadratic in the Weyl conformal curvature, may well be a viable alternative to Einstein gravity as the fundamental theory of gravitation. The present investigation is concerned with an examination of the uniqueness and stability of spherically symmetric solutions of classical conformal gravity. In Einstein gravity, Birkhoff's theorem guarantees that the most general spherically symmetric, electrovac solution of the Einstein-Maxwell equations is static. It appears plausible, and provable, that conformal gravity admits a Birkhoff theorem. The theorem is stated in a form analogous to its statement in Einstein gravity, and a proof of the conformal-gravity Birkhoff theorem is discussed.