Algebraic determination of the metric from the curvature in general relativity
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The general solution for a symmetric second-order tensorX of the equationXe(aR e b cd=0 whereR is the Riemann tensor of a space-time manifold, andX is obtained in terms of the curvature 2-form structure ofR by a straightforward geometrical technique, and agrees with that given by McIntosh and Halford using a different procedure. Two results of earlier authors are derived as simple corollaries of the general theorem.
KeywordsManifold Field Theory General Relativity Elementary Particle Quantum Field Theory
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