Does Birkhoff's theorem apply to rotating collapsing stars? Birkhoff's theorem states that every spherically symmetric vacuum solution to
 $R_{\alpha\beta} = 0$ is static, which greatly assists in the solution to the Schwarzschild solution by eliminating time derivatives.
For collapsing stars with angular momentum, (i.e. all real ones, as far as I know), is this theorem applicable? 
I ask this because I am not sure if real stars collapse in a sufficiently spherical manner.
I am  presuming, and I am open to correction on this, that a rotating star's angular momentum would result in an equatorial bulge, with a non spherically symmetrical collapse. In particular, would this have consequences for the formation of black holes?
 A: The theorem does not apply, as we do not have spherical symmetry. All we have is rotational symmetry about a preferred axis.
In fact, the gravitational field outside a rotating object will be Kerr, which only reduces to Schwarzschild in the case of no rotation. Otherwise, there will be time-space terms in the metric, making it not static. Still, Kerr is stationary, meaning the metric does not depend on time ($\partial_0 g_{\mu\nu} = 0$).
As a matter of fact, rotation is far from negligible in most contexts of astrophysical collapse. Things generally have too much angular momentum to collapse further, and this is true even of stars becoming black holes. For some rough numbers, the Sun has a mass $M = 2\times10^{30}\ \mathrm{kg}$, a radius $R = 7\times10^8\ \mathrm{m}$, and a period $P = 25\ \mathrm{days}$. Approximating it as a uniform sphere undergoing uniform rotation, it has an angular momentum
$$ L = \frac{4\pi MR^2}{3P} = 2\times10^{42}\ \mathrm{kg\cdot m^2/s}. $$
A Kerr black hole cannot have $cL/GM^2$ exceed $1$, or else there would be a naked singularity. But $cL/GM^2 \approx 2$ for the Sun.
Not only are real black holes expected to have some rotation (and therefore not be Schwarzschild), it would not be surprising to find most of them coming close to the upper bound on how fast they can spin.
