A pure geometric field theory with parameterized canonical W-tensor

This paper presents a pure geometric field theory within the framework of Parameterized Absolute Parallelism geometry, aiming to exceed the limitations of both Riemannian and Absolute Parallelism geometries. Following the Unification Principle, the theory employs Parameterized Absolute Parallelism geometry, which involves a linear connection with nonvanishing torsion, nonvanishing curvature and nonvanishing W-tensor. The presented theory is constructed following the Dolan–McCrea variational method to derive the field equations. The theory is shown to incorporate gravity and electromagnetic features. By studying the connection between physical quantities and geometric objects, Poisson and Laplace equations are obtained in the linearized version of the theory. In free space, the Schwarzschild exterior solution of general relativity holds in the present theory.