Premetric equivalent of general relativity: Teleparallelism
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.
Cite
@article{arxiv.1611.05759,
title = {Premetric equivalent of general relativity: Teleparallelism},
author = {Yakov Itin and Friedrich W. Hehl and Yuri N. Obukhov},
journal= {arXiv preprint arXiv:1611.05759},
year = {2017}
}
Comments
Some corrections made in accordance with criticisms of the referee, references added; this version supersedes the printed version (it contains some slips due to the editorial policy)