The teleparallel equivalent of general relativity

By J. Maluf. 2013

601 citations recorded by the source corpus.

A review of the teleparallel equivalent of general relativity is presented. It is emphasized that general relativity may be formulated in terms of the tetrad fields and of the torsion tensor, and that this geometrical formulation leads to alternative insights into the theory. The equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations. The review starts with a brief account of the history of teleparallel theories of gravity. Then the ordinary interpretation of the tetrad fields as reference frames adapted to arbitrary observers in space–time is discussed, and the tensor of inertial accelerations on frames is obtained. It is shown that the Lagrangian and Hamiltonian field equations allow us to define the energy, momentum and angular momentum of the gravitational field, as surface integrals of the field quantities. In the phase space of the theory, these quantities satisfy the algebra of the Poincaré group.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/522bec6d64b926b2e2af8064e016f3273f69f67f

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Citations in the corpus

Bouncing cosmology in f(Q) symmetric teleparallel gravity (2020, background): “In this case, a more general affine structure has to be considered, the so called Weitzenböck connection [38–40].”
f(T) teleparallel gravity and cosmology (2015, background): “The problem of the localization of the gravitational energy-momentum tensor has been discussed in detail in [129].”
Generalized Curvature-Matter Couplings in Modified Gravity (2014, methodology): “The latter approach has been denoted the “Teleparallel Equivalent of General Relativity” (TEGR) [30–35] and consists of replacing the torsion-less Levi–Civita connection by the curvature-less Weitzenböck one and using the vierbein instead of the metric as the fundamental field.”
Dynamical systems applied to cosmology: Dark energy and modified gravity (2017, neutral): “Note that we are following the standard approach in teleparallel gravity where the spin connection is set to zero (see e.g. Maluf (2013)), rather than the covariant approach where the spin connection plays a more active role (Krššák & Saridakis, 2016).”
Stellar structure models in modified theories of gravity: Lessons and challenges (2019, background): “Another family of extensions of GR is based upon the teleparallel equivalent of GR, where the main geometrical ingredient is torsion instead of curvature [306].”
Teleparallel theories of gravity: illuminating a fully invariant approach (2018, background): “Now, there is in the literature a different approach to teleparallel gravity, known as pure tetrad teleparallel gravity (see [34] for a review).”
Teleparallel Palatini theories (2018, methodology): “While the second alternative would lead to the framework of Einstein-Cartan theory, the first option is the standard prescription used in TEGR [5, 13, 14].”