Five-dimensional unified field theory: The source function

In Kaluza's five-dimensional unified field theory the restriction for the 55 component of the metric tensor ₅₅=1 demands that the 15 equations for the unified field be weakened. Equations which have been proposed have identically vanishing trace. The equations then admit only a radiation field as source of the gravitational field. By relaxing the condition, this limitation is avoided, while retaining the striking successes of the five-dimensional approach. A scalar function, determined by the 15th field equation apart from integration constants, provides source terms for both the gravitational and electromagnetic fields, in the latter case of polarization type.