Extensions of Birkhoff’s Theorem in 6D Gauss‐Bonnet Gravity

We present a generalization of Birkhoff’s theorem in the context of six‐dimensional Gauss‐Bonnet theory. Contrary to what we encounter in ordinary General Relativity, the presence of the higher curvature terms leads to novel constraints on the geometry of the admissible black hole horizons. As a result, we can have static solutions which depart from spherical symmetry, but must satisfy specific constraints involving the Weyl tensor of the four‐dimensional horizon. After obtaining the general profile of the static solutions in the transverse space, we give explicit examples of such black hole horizons, which are in general of an anisotropic nature.