Metric-affine approach to teleparallel gravity

By Yuri N. Obukhov, J. G. Pereira. 2002

203 citations recorded by the source corpus.

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 Weitzenb\"ock 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 teleparallelism. We present a systematic treatment of 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ab84f128a4528f0e2b670ab81fb36b990e34be66

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Citations in the corpus

Teleparallel Palatini theories (2018, background): “In the frame formalism of teleparallelism, the so called λ-symmetry was clarified in the Hamiltonian formulation [66, 67], see yet [33] for a subtle remark, and [32] for the additional symmetry in the metric-affine extension of the Poincaré extension.”
Teleparallel theories of gravity: illuminating a fully invariant approach (2018, methodology): “It is worth noting that alternatively one could set up an action for teleparallel theories and through the use of Lagrange multipliers ensure that the curvature of the spin connection is zero via a metric affine gauge approach [132, 133].”
Elie Cartan's torsion in geometry and in field theory, an essay (2007, background): “The dynamical contents of the model was later studied by Schweizer et al. [92], Nitsch and Hehl [69], Meyer [61], and more recent advances can be found in Aldrovandi andPereira [1], Andrade and Pereira [2], Gronwald [23], Itin [42, 43], Maluf and da Rocha-Neto [56], Muench [65], Obukhov and Pereira ”
A systematic approach to generalisations of General Relativity and their cosmological implications (2018, methodology): “connection of the parallelisation being the Weitzenböck connection with vanishing curvature) the minimal coupling procedure fails for fermions [76].”
Gauge Theories Of Gravitation: A Reader With Commentaries (2013, methodology): “For reference purposes we display the most general quadratic Lagrangian,3 see [14], Eq.”
On the covariance of teleparallel gravity theories (2017, background): “For this version of teleparallel gravity, see also the book of Blagojević [5], and for the implementation in metric-affine gravity, the paper [24].”