Exterior-Algebraic Derivation of Einstein Field Equations Employing a Generalized Basis

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Abstract
A tetrad vector formulation of Einstein's field equations is developed in which the orthogonality properties of the tetrad are permitted to vary in any prescribed smooth way from one space-time point to another. The components of the Riemann tensor with respect to such a basis are derived by means of exterior calculus. The approach facilitates a simple direct derivation of the Harrison-Ernst equations.