  The metric of a spacetime can be greatly simplified if the spacetime is
circular. We prove that in generic effective theories of gravity, the spacetime
of a stationary, axisymmetric and asymptotically flat solution must be circular
if the solution can be obtained perturbatively from a solution in the general
relativity limit. This result applies to a broad class of gravitational
theories that include arbitrary scalars and vectors in their light sector, so
long as their nonstandard kinetic terms and nonmininal couplings to gravity are
treated perturbatively.
