as a byproduct. New teleparallel gravity theory New teleparallel gravity theory (or new general relativity) is a theory of gravitation on Weitzenböck spacetime, and attributes gravitation to the torsion tensor formed of the parallel vector fields. In the new teleparallel gravity theory the fundamental assumptions are as follows: In 1961 Christian Møller revived Einstein's idea, and Pellegrini and Plebanski found a Lagrangian formulation for absolute parallelism. Møller tetrad theory of gravitation In 1961, Møller showed that a tetrad description of gravitational fields allows a more rational treatment of the energy-momentum complex than in a theory based on the metric tensor alone. The advantage of using tetrads as gravitational variables was connected with the fact that this allowed to construct expressions for the energy-momentum complex which had more satisfactory transformation properties than in a purely metric formulation. In 2015, it has been shown that total energy of matter and gravitation is proportional to the Ricci scalar of three-space up to linear order of perturbation. New translation teleparallel gauge theory of gravity Independently in 1967, Hayashi and Nakano revived Einstein's idea, and Pellegrini and Plebanski started to formulate the gauge theory of the space-time translation group. Hayashi pointed out the connection between the gauge theory of the spacetime translation group and absolute parallelism. The first fiber bundle formulation was provided by Cho. This model was later studied by Schweizer et al., Nitsch and Hehl, Meyer, and more recent advances can be found in Aldrovandi and Pereira, Gronwald, Itin, Maluf and da Rocha Neto, Münch, Obukhov and Pereira, and Schucking and Surowitz. Nowadays, people study teleparallelism purely as a theory of gravity without trying to unify it with electromagnetism. In this theory, the gravitational field turns out to be fully represented by the translational gauge potential , as it should be for a gauge theory for the translation group. If this choice is made, then there is no longer any Lorentz gauge symmetry because the internal Minkowski space fiber—over each point of the spacetime manifold—belongs to a fiber bundle with the Abelian as structure group. However, a translational gauge symmetry may be introduced thus: Instead of seeing tetrads as fundamental, we introduce a fundamental translational gauge symmetry instead (which acts upon the internal Minkowski space fibers affinely so that this fiber is once again made local) with a connection and a "coordinate field" taking on values in the Minkowski space fiber. More precisely,