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Extensions of Birkhoff's Theorem in six-dimensional Gauss-Bonnet Gravity

We discuss a generalization of Birkhoff's theorem in the case of six-dimensional Einstein-Gauss-Bonnet gravity with a cosmological constant. The process starts similarly to the five-dimensional case : two classes of solutions are found, one being the usual static black holes solutions, the other remaining partially undetermined due to a fine tuning of the theory. However, the horizon structure is severely constrained by the equations of motion of 6D Gauss-Bonnet gravity, and its characteristics appear explicitly in the black hole potential, radically departing from the five-dimensional case. We then give some examples of such non-trivial horizon geometries.

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