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

TL;DR

This paper proves that in broad effective theories of gravity, stationary, axisymmetric, asymptotically flat solutions are necessarily circular if they are perturbatively close to solutions in general relativity, simplifying their analysis.

Contribution

It establishes a general perturbative criterion for the circularity of black hole spacetimes in diverse gravitational theories.

Findings

Stationary, axisymmetric solutions are circular under perturbations from GR.

The result applies to theories with scalars and vectors with nonstandard kinetic terms.

Simplifies the study of black holes in modified gravity theories.

Abstract

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.