Zero Curvature Tensor in Einstein's Unified Field Theory

Abstract

In classical relativistic gravitational theory a zero curvature tensor is characteristic of the flat space-time of special relativity. However this result is not valid in Einstein's forms of unified field theory. Our present paper derives and discusses all solutions of Einstein's unified field equations that result from a zero curvature tensor.By obtaining a rather extensive class of rigorous solutions we had hoped that a detailed examination of their physical interpretations might clarify many of the ambiguities that exist, in the theory, at the present time. This hope was not realized as the detailed examination served to show that the present formulations of Einstein's unified field theories cannot be considered complete.