Editing Teleparallelism (section)

==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:

{{ordered list|list_style_type=upper-alpha
|Underlying spacetime is the Weitzenböck spacetime, which has a quadruplet of parallel vector fields as the fundamental structure. These parallel vector fields give rise to the metric tensor as a by-product. All physical laws are expressed by equations that are covariant or form invariant under the group of general coordinate transformations.
|The [[equivalence principle]] is valid only in classical physics.
|Gravitational field equations are derivable from the action principle.
|The field equations are partial differential equations in the field variables of not higher than the second order.}}

In 1961 [[Christian Møller]]<ref name=moeller/> revived Einstein's idea, and Pellegrini and Plebanski<ref name=pellegrini /> found a Lagrangian formulation for ''absolute parallelism''.

=== Møller tetrad theory of gravitation ===
In 1961, Møller<ref name=moeller>{{cite journal|last=Møller|first=Christian|date=1961|title=Conservation laws and absolute parallelism in general relativity|journal=Mat. Fys. Dan. Vid. Selsk.|volume=1|pages=1–50|issue=10}}</ref><ref>{{cite journal| last=Møller |first=Christian |date=1961 |title=Further remarks on the localization of the energy in the general theory of relativity|journal=Ann. Phys.|volume=12|pages=118–133| doi=10.1016/0003-4916(61)90148-8|issue=1|bibcode = 1961AnPhy..12..118M }}</ref> showed that a [[Frame fields in general relativity|tetrad]] description of gravitational fields allows a more rational treatment of the [[Stress–energy–momentum pseudotensor|energy-momentum complex]] than in a theory based on the [[Metric tensor (general relativity)|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 was shown that the total energy of matter and gravitation is proportional to the [[Ricci scalar]] of three-space up to the linear order of perturbation.<ref>{{Cite journal| last1=Abedi|first1=Habib| last2=Salti|first2=Mustafa| date=2015-07-31| title=Multiple field modified gravity and localized energy in teleparallel framework|journal=General Relativity and Gravitation| language=en | volume=47|issue=8|pages=93|doi=10.1007/s10714-015-1935-z| issn=0001-7701| bibcode=2015GReGr..47...93A | s2cid=123324599 }}</ref>