Covariant double-null dynamics: 2 + 2-splitting of the Einstein equations

We develop a (2 + 2)-imbedding formalism adapted to a double foliation of spacetime by a net of two intersecting families of lightlike hypersurfaces. The intersections define a set of 2-spaces with hypersurface-orthogonal lightlike normals. The formalism is two-dimensionally covariant, and leads to simple, geometrically transparent and tractable expressions for the Einstein field equations and the Einstein - Hilbert action, and it should find a variety of applications. It is applied here to elucidate the structure of the characteristic initial-value problem of general relativity.