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.

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)

References in corpus (6)

• The teleparallel equivalent of general relativity
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Cited by in corpus (22)

• Teleparallel Gravity: From Theory to Cosmology
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Conformal Gravity and Transformations in the Symmetric Teleparallel Framework
• Teleparallel theories of gravity as analogue of non-linear electrodynamics
• Propagation of gravitational waves in teleparallel gravity theories
• Hamiltonian and primary constraints of new general relativity
• Quest for the extra degree of freedom in f(T) gravity
• Scalar-torsion theories of gravity II: $L(T,X,Y,\varphi )$ theory
• Parameterized post-Newtonian limit of general teleparallel gravity theories
• Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection?
• Premetric teleparallel theory of gravity and its local and linear constitutive law
• An axiomatic purification of gravity
• Geometry and covariance of symmetric teleparallel theories of gravity
• General relativity as a special case of Poincaré gauge gravity
• Classification of primary constraints for new general relativity in the premetric approach
• Decomposition of third-order constitutive tensors
• Conservation of energy-momentum of matter as the basis for the gauge theory of gravitation
• Physical dimensions/units and universal constants: their invariance in special and general relativity
• On the bundle of Clifford algebras over the space of quadratic forms
• Self-Excited Gravitational Instantons
• Singular teleparallelism
• On the risk of premature unification