Birkhoff's theorem with cosmological constant

[pervect]

Birkhoff's theorem says that any vacuum solution of Einstein's equations must be static, and asymptotically flat.

One of the consequences of Birkhoff's theorem is that the gravitational field inside any spherical shell of matter is zero, even if the shell is expanding.

But what happens if we allow a cosmological constant? Can we still say that the field inside a spherical shell of matter (including expanding shells) is zero if we assume that the universe has a non-zero cosmological constant?