Abstracto
- It is shown that in an algebraically special space‐time which admits a congruence of null strings, a source‐free gauge field aligned with the congruence is determined by a matrix potential which has to satisfy a second‐order differential equation with quadratic nonlinearities. The Einstein–Yang–Mills equations are then reduced to a scalar and two matrix equations. In the case of self‐dual gauge fields in a self‐dual space‐time, the existence of an infinite set of conservation laws, of an associated linear system, and of infinitesimal Bäcklund transformations is demonstrated. All the results apply for an arbitrary gauge group.