A purely geometric field theory unifying gravity and electromagnetism in absolute parallelism ^*

Abstract

Abstract A geometric field theory unifying gravity and electromagnetism is constructed in absolute parallelism (AP) geometry, satisfying the covariance and unification principles. The theory is purely geometric, defining all fields and physical quantities in terms of AP geometry. The field equations are derived from a Lagrangian density based on a conformally invariant curvature tensor of a conformal connection. These equations are obtained using a general differential identity that represents the conservation law in AP geometry. The physical properties of the theory are investigated using three distinct methods, demonstrating its ability to describe gravity, electromagnetism, and matter distribution. The linearized field equations of the theory yield the Poisson and Laplace equations governing the material and charge distributions. The theory is reduced to general relativity under certain conditions. Moreover, the theory implies a non-minimal coupling between gravity and material distributions.