A stationary black hole must be axisymmetric in effective field theory

TL;DR

This paper extends the black hole rigidity theorem to effective field theories of vacuum gravity, demonstrating that stationary black holes must be axisymmetric under broad theoretical conditions.

Contribution

It generalizes the classical rigidity theorem to a wide class of diffeomorphism invariant effective field theories of gravity.

Findings

The theorem applies to any such effective field theory with a UV scale.

Stationary black holes in these theories are necessarily axisymmetric.

The extension relies on local power series expansions in the UV scale.

Abstract

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.