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Metric-affine approach to teleparallel gravity

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arxiv gr-qc/0212080 v1 pith:JEDVMLRW submitted 2002-12-19 gr-qc

Yu. N. Obukhov , J. G. Pereira This is my paper · ORCID
classification gr-qc
keywords teleparallelgeneralgravitymetric-affinespacetimetheoryapproachcase
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The teleparallel gravity theory, treated physically as a gauge theory of translations, naturally represents a particular case of the most general gauge-theoretic model based on the general affine group of spacetime. On the other hand, geometrically, the Weitzenboeck spacetime of distant parallelism is a particular case of the general metric-affine spacetime manifold. These physical and geometrical facts offer a new approach to the teleparallelism. We present a systematic treatment of the teleparallel gravity within the framework of the metric-affine theory. The symmetries, conservation laws and the field equations are consistently derived, and the physical consequences are discussed in detail. We demonstrate that the so-called teleparallel GR-equivalent model has a number of attractive features which distinguishes it among the general teleparallel theories, although it has a consistency problem when dealing with spinning matter sources.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Scale-invariant Schr\"{o}dinger geometry in symmetric teleparallel gravity

    gr-qc 2026-07 conditional novelty 6.0 of 10

    A quadratic nonmetricity action of Schrödinger type is locally scale-invariant exactly when its Palatini connection equations admit the length-preserving Schrödinger connection.

  2. Horizon Singularities in the Schwarzschild Geometry of the Teleparallel Equivalent of General Relativity

    gr-qc 2026-06 unverdicted novelty 6.0 of 10

    Schwarzschild TEGR geometries split into regular and singular subclasses by Lorentz sector; regular ones have finite torsion invariants at the horizon and admit analytic extensions.

  3. On non-vacuum black holes in new general relativity

    gr-qc 2026-02 unverdicted novelty 6.0 of 10

    New general relativity does not admit physically meaningful non-trivial black holes distinct from those of the teleparallel equivalent of general relativity.

  4. Revisiting Coincident GR in Internal STEGR Formulation

    gr-qc 2025-06 conditional novelty 5.0 of 10

    The paper derives internal-STEGR field equations, recovers coincident GR as the coincident-gauge sector, and finds that massive test particles obey a norm-flow equation instead of geodesics.

  5. On black holes in new general relativity

    gr-qc 2025-08 unverdicted novelty 4.0 of 10

    All viable NGR models, including TEGR and 1P-H&S, exhibit divergences in torsion scalars at local horizons, obstructing black hole interpretations.

  6. Teleparallel gravity from the principal bundle viewpoint

    gr-qc 2025-07 unverdicted novelty 3.0 of 10

    TEGR is argued to admit a gauge theory formulation on principal bundles with Poincaré or Lorentz structure groups, where the gauge group is the diffeomorphism group if the teleparallel connection is not treated as an ...

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