Representation of the Einstein-Proca field by an A₄*

The Einstein-Proca field is 'geometrised' in the sense that the joint field equations are generated by a variational principle, the Lagrangian of which is solely a certain function of curvature quantities and the metric tensor g ij of an A 4 *, i.e. of a linearly connected space A 4 with symmetric connection on which an additional symmetric tensor field g ij is defined.