Formation of trapped surfaces for the spherically symmetric Einstein-Yang-Mills system with non-trivial incoming data

We establish a trapped surface formation theorem for the spherically symmetric Einstein Yang Mills equations in a double-null gauge. The theorem concerns characteristic initial data posed on a pair of transversely intersecting null hypersurfaces and allows nontrivial incoming data. The proof extends the singular characteristic method of An and Lim for the Einstein Maxwell Charged Scalar Field System to the non-abelian Yang Mills setting, where the curvature coupling and gauge field nonlinearities introduce new structural difficulties. This paper constitutes the first part of a program toward weak cosmic censorship for the Einstein Yang Mills system.