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Metric-affine variational principles in general relativity. I. Riemannian space-time
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In this article, the Lagrange multiplier which effects this constraint, the hypermomentum current, is closely related to the constraint "force" which keeps space-time Riemannian.Abstract:
Within the confines of conventional general relativity, variational principles are analyzed in which the metric tensor and the asymmetric linear connection are varied independently. The constraint that space-time remain Riemannian is introduced by means of the Lagrange multiplier technique. The Lagrange multiplier which effects this constraint, the hypermomentum current, is closely related to the constraint “force” which keeps space-time Riemannian and should be a measure for the violation of the Riemannian constraint at the microscopic level.read more
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f ( R ) theories of gravity
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f(R) theories
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Extended Theories of Gravity
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Metric affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance
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References
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The classical theory of fields
TL;DR: The principle of relativity Relativistic mechanics Electromagnetic fields electromagnetic waves as discussed by the authors The propagation of light The field of moving charges Radiation of electromagnetic waves Particle in a gravitational field The gravitational field equation
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The Einstein Tensor and Its Generalizations
TL;DR: In this paper, the number of independent tensors of this type depends crucially on the dimension of the space, and, in the four dimensional case, the only tensors with these properties are the metric and the Einstein tensors.
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General Relativity with Spin and Torsion: Foundations and Prospects
TL;DR: In this article, a generalization of Einstein's gravitational theory is discussed in which the spin of matter as well as its mass plays a dynamical role, and the theory which emerges from taking this coupling into account, the ${U}_{4}$ theory of gravitation, predicts, in addition to the usual infinite-range gravitational interaction medicated by the metric field, a new, very weak, spin contact interaction of gravitational origin.