Premetric equivalent of general relativity: Teleparallelism

Nov 17, 2016
13 pages
Published in:
  • Phys.Rev.D 95 (2017) 8, 084020
  • Published: Apr 12, 2017
e-Print:

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Abstract: (arXiv)
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.
Note:
  • 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)
  • gravitation: potential
  • invariance: Lorentz
  • group: translation
  • space-time: tensor
  • gauge field theory
  • general relativity
  • field equations
  • topological
  • teleparallel
  • gravitation: model