1 O ct 1 99 2 RESEARCH ANNOUNCEMENT

We consider the Einstein/Yang-Mills equations in 3 + 1 space time dimensions with SU(2) gauge group and prove rigorously the existence of a globally defined smooth static solution. We show that the associated Einstein metric is asymp-totically flat and the total mass is finite. Thus, for non-abelian gauge fields the Yang/Mills repulsive force can balance the gravitational attractive force and prevent the formation of singularities in spacetime. 1 2 Rg ij = 0 is the celebrated Schwarzschild metric that is singular at r = 0 [1]. Despite this defect, this solution has applicability for large r to physical problems, e.g., the perihelion shift of Mercury. Similarly, the Yang/Mills equations d * F = 0, which unify electromagnetic and nuclear forces, have no static regular solutions on R 4 [3]. Furthermore, if one couples Einstein's equations to Maxwell's equations, to unify gravity and electromagnetism (1) R ij − 1 2 Rg ij = σT ij , d * F = 0 (T ij is the stress-energy tensor relative to the electromagnetic field F ij), the only static solution is the Reissner-Nordström metric, which is again singular at the origin [1]. Finally, the Einstein-Yang/Mills (EYM) equations, which unify gravita-tional and nuclear forces, were shown in [4] to have no static regular solutions in (2 + 1) space time dimensions for any gauge group G. We announce here that the contrary holds in (3 + 1) space-time dimensions. Indeed, with SU(2) gauge group