Involutive pre-Maxwellian structures in general relativity

Conditions are stated under which a structure (M, g, F, L), where M is a four-dimensional differentiable manifold, g a Lorentz metric, F a regular 2-form on M, and L a tensor field of prescribed type, is pre-Maxwellian and involutive. A theorem is proved stating that if a structure is involutive pre-Maxwellian, then there exists an Abelian group G2 of isometries which is also involutive. The results enable a statement on the form of the type D solutions of the Maxwell-Einstein equations with cosmological constant and nonsingular electromagnetic field at coincidence.