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arXiv · 1611.05759

Premetric equivalent of general relativity: Teleparallelism

Yakov Itin·Friedrich W. Hehl·Yuri N. Obukhov
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Abstract

In general relativity (GR), the metric tensor of spacetime is essential since it represents the gravitational potential. In other gauge theories (such as electromagnetism), the so-called premetric approach succeeds in separating the purely topological field equation from the metric-dependent constitutive law. We show here that GR allows for a premetric formulation, too. For this purpose, we apply the teleparallel approach of gravity, which represents GR as a gauge theory based on the translation group. We formulate the metric-free topological field equation and a general linear constitutive law between the basic field variables. The requirement of local Lorentz invariance turns the model into a full equivalent of GR. Our approach opens a way for a natural extension of GR to diverse geometrical structures of spacetime.

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Yakov Itin, Friedrich W. Hehl, Yuri N. Obukhov. 2016-11-17. Premetric equivalent of general relativity: Teleparallelism. https://doi.org/10.1103/physrevd.95.084020

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