Biframe bundle geometry: An extension of Rainich-Misner-Wheeler theory to include sources

Recently the original theory of Rainich, Misner, and Wheeler (RMW) has been shown to have a natural reformulation in terms of a new principal fiber bundle, namely the bundle of biframesL²M over spacetime. We extend this new formalism further and show that the original RMW program can be generalized to include Einstein-Maxwell spacetimes with geometrical sources. The assumptions of a Riemannian connection one-form on the linear frame bundleLM and a general connection one-form onL²M necessarily imply the existence of a difference formK. A generalization of the standard RMW theorem is developed which provides the necessary and sufficient conditions on an arbitrary triple (M, g, K) in order for this triple to be an Einstein-Maxwell spacetime with geometrical sources. All sources for the field equations associated with such spacetimes are geometrical, as they are constructible from the metricg, the difference formK, and their derivatives. The extension of the RMW program presented here introduces a second complexion vector, in addition to the standard RMW complexion vector, and the formalism reduces, in the special case of no sources, to the standard RMW program.