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Energy-Momentum and Equivalence Principle in Non-Riemannian Geometries

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Abstract

We introduce an energy-momentum density vector which is independent of the affine structure of the manifold and whose conservation is linked to observers. Integrating this quantity over time-like surfaces we can define Hamiltonian and momentum for the system which coincide with the corresponding ADM definitions for the case of irrotational Riemannian manifolds. As a consequence of our formalism, a Weak Equivalence Principle version for manifolds with torsion appears as the natural extension to non-Riemannian geometries from the Equivalence Principle of General Relativity.

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Authors
  1. M. Castagnino
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  2. M. L. Levinas
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  3. N. Umérez
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Castagnino, M., Levinas, M.L. & Umérez, N. Energy-Momentum and Equivalence Principle in Non-Riemannian Geometries. General Relativity and Gravitation 29, 691–703 (1997). https://doi.org/10.1023/A:1018877620865

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  • DOI: https://doi.org/10.1023/A:1018877620865

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