Einstein/Yang-Mills Equations

Abstract

In this paper, we shall describe some recent results, ([6,7]), concerning the existence of smooth, globally defined static solutions of the Einstein /Yang-Mills (EYM) equations. The EYM equations extend Einstein’s celebrated gravitational field equations, to include other “force” fields: electromagnet ism, and the weak and strong nuclear force fields. It turns out that solutions of such coupled systems of equations, in n = 4 space-time dimensions, have some very interesting mathematical and physical properties. Thus for the non-abelian gauge group G = SU (2), we can prove the existence of infinitely many non-singular globally defined solutions - a result that fails to hold if G = U (1), (the coupling of gravity to electromagnetism). Since the (classical) Yang-Mills equations with G = SU (2) correspond to the weak nuclear force, our result indicates that coupling gravity to the weak nuclear force can prevent singularity formation in space-time. Furthermore, these solutions give rise to constants which correspond to masses. In other words, numbers representing masses are a direct consequence of our theory, and need not be prescribed in an ad-hoc manner - as is usually done in physical theories.