The teleparallel equivalent of general relativity

Abstract

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 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.

41 pages, 1 figure, published by the Annalen der Physik

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Cited by in corpus (26)

• $f(T,\mathcal{T})$ gravity and cosmology
• Generalized curvature-matter couplings in modified gravity
• Teleparallel equivalent of Gauss-Bonnet gravity and its modifications
• Nonminimal torsion-matter coupling extension of f(T) gravity
• Noether Symmetry Approach in $f(T,B)$ teleparallel cosmology
• Dynamical behavior in $f(T,T_G)$ cosmology
• Cosmological applications of $F(T,T_G)$ gravity
• Dynamical features of scalar-torsion theories
• $f(T)$ gravitational baryogenesis
• Stability of the flat FLRW metric in $f(T)$ gravity
• Self-Gravitating Spherically Symmetric Solutions in Scalar-Torsion Theories
• FRW in quadratic form of $f(T)$ gravitational theories
• Generalized teleparallel cosmology and initial singularity crossing
• Hamiltonian formulation of teleparallel gravity
• Kerr geometry in f(T) gravity
• Growth factor in $f(T,\mathcal{T})$ gravity
• Energy conditions in $f(T)$ gravity with non-minimal torsion-matter coupling
• Nonlocal Gravity: The General Linear Approximation
• On Kottler's path: origin and evolution of the premetric program in gravity and in electrodynamics
• Born-Infeld and Charged Black Holes with non-linear source in $f(T)$ Gravity
• Nonminimally coupled scalar field in teleparallel gravity: boson stars
• Weitzenböck's Torsion, Fermi Coordinates and Adapted Frames
• Spherical collapse and virialization in $f(T)$ gravities
• Bondi-Sachs energy-momentum and the energy of gravitational radiation
• Nonlocal General Relativity
• Bi-connected Gravity Fields