Particle-like platonic solutions in scalar gravity

Abstract We construct globally regular gravitating solutions, which possess only discrete symmetries. These solutions of Yang–Mills-dilaton theory may be viewed as exact (numerical) solutions of scalar gravity, by considering the dilaton as a kind of scalar graviton, or as approximate solutions of Einstein–Yang–Mills theory. We focus on platonic solutions with cubic symmetry, related to a rational map of degree N = 4 . We present the first two solutions of the cubic N = 4 sequence, and expect this sequence to converge to an extremal Reissner–Nordstrom solution with magnetic charge P = 4 .