“Cusp” solutions in Gauss-Bonnet gravity

Einstein-dilaton-Gauss-Bonnet gravity is investigated for the existence of solutions with mild singularities, not shielded by the event horizons. These still may have sense since presumably such singularities will be smoothed by corrections to the Einstein theory from quantum gravity/string theory. We show that gravity with a first-order correction, the Gauss-Bonnet term, gives rise to special types of singularities, which we call cusps, with powers 1/2 and 1/3 in a series expansion. The full space then can be split into several regions with classically impenetrable borders, and/or a flat asymptotic.