Obstructions on the horizon geometry from string theory corrections to Einstein gravity

Higher-dimensional Einstein gravity in vacuum admits static black hole solutions with an Einstein manifold of nonconstant curvature as a horizon. This gives a much richer family of static black holes than in four-dimensional GR. However, as we show in this Letter, the Gauss-Bonnet string theory correction to Einstein gravity poses severe limitations on the geometry of a horizon Einstein manifold. The additional stringy constraints rule out most of the known examples of exotic black holes with a horizon of nonconstant curvature.