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The metric of a spacetime can be greatly simplified if the spacetime iscircular. We prove that in generic effective theories of gravity, the spacetimeof a stationary, axisymmetric and asymptotically flat solution must be circularif the solution can be obtained perturbatively from a solution in the generalrelativity limit. This result applies to a broad class of gravitationaltheories that include arbitrary scalars and vectors in their light sector, solong as their nonstandard kinetic terms and nonmininal couplings to gravity aretreated perturbatively.

Square Peg in a Circular Hole: Choosing the Right Ansatz for Isolated Black Holes in Generic Gravitational Theories