'Cusp' solutions in Gauss-Bonnet gravity

Einstein-dilaton-Gauss-Bonnet gravity is investigated on 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 Einstein theory from quantum gravity/string theory. We show that gravity with the first-order correction, the Gauss--Bonnet term, gives rise to special types of singularities, which we call 'cusps', with 1/2-th and 1/3-th powers in series expansion. The full space then can be split onto several cusps with classically impenetrable borders, and/or flat asymptotic.