  The black hole rigidity theorem asserts that a rotating stationary black hole
must be axisymmetric. This theorem holds for General Relativity with suitable
matter fields, in four or more dimensions. We show that the theorem can be
extended to any diffeomorphism invariant theory of vacuum gravity, assuming
that this is interpreted in the sense of effective field theory, with coupling
constants determined in terms of a ``UV scale'', and that the black hole
solution can locally be expanded as a power series in this scale.
