Null-tetrad formulation of the Yang-Mills field equations

The Yang-Mills dynamical variables in the presence of gravitation are presented in terms of new variables by means of a null-tetrad and spin coefficient method. The Yang-Mills equations in curved space are consequently written in the null-tetrad method. The resulting equations then resemble the Newman-Penrose version of Maxwell's equations extended to a non-Abelian gauge group. A special consideration is then given to the flat-space case, thus recovering the usual Yang-Mills theory, but now written in the null-tetrad method. The advantages of the new approach to the Yang-Mills equations are illustrated by considering the problem of exact solutions of these equations both in the presence and in the absence of gravitation.