Editing Nonsymmetric gravitational theory

{{Short description|Concept in physics}}
In [[theoretical physics]], the '''nonsymmetric gravitational theory'''<ref name=Moffat1995>{{Citation
 | title = Nonsymmetric Gravitational Theory
 | journal = Phys. Lett. B
 | volume = 355
 | issue = 3–4
 | date = 1995
 | pages = 447–452
 | author = J. W. Moffat
 | doi = 10.1016/0370-2693(95)00670-G |bibcode = 1995PhLB..355..447M
 | arxiv=gr-qc/9411006| s2cid = 15879285
 }}</ref> ('''NGT''') of [[John Moffat (physicist)|John Moffat]] is a [[Classical mechanics|classical]] theory of [[gravitation]] that tries to explain the observation of the flat [[Galaxy rotation curve|rotation curves of galaxies]].

In [[general relativity]], the gravitational field is characterized by a [[symmetric tensor|symmetric]] rank-2 [[tensor]], the [[metric tensor (general relativity)|metric tensor]]. The possibility of generalizing the metric tensor has been considered by many, including [[Albert Einstein]] and others. A general (nonsymmetric) tensor can always be decomposed into a symmetric and an [[antisymmetric tensor|antisymmetric]] part. As the [[electromagnetic field]] is characterized by an antisymmetric rank-2 tensor, there is an obvious possibility for a [[unified field theory|unified theory]]: a nonsymmetric tensor composed of a symmetric part representing gravity, and an antisymmetric part that represents [[electromagnetism]]. Research in this direction ultimately proved fruitless; the desired classical unified field theory was not found.

In 1979, Moffat made the observation<ref name=Moffat1979>{{Citation
 | title = New theory of gravitation
 | journal = Phys. Rev. D
 | date = 1979
 | volume = 19
 | issue = 12
 | pages = 3554–3558
 | author = J. W. Moffat
 | doi = 10.1103/PhysRevD.19.3554 |bibcode = 1979PhRvD..19.3554M }}</ref> that the antisymmetric part of the generalized metric tensor need not necessarily represent electromagnetism; it may represent a new, hypothetical force. Later, in 1995, Moffat noted<ref name=Moffat1995/> that the field corresponding with the antisymmetric part need not be massless, like the electromagnetic (or gravitational) fields.

In its original form, the theory may be unstable, although this has only been shown in the case of the linearized version.<ref name=Ragusa1997>{{Citation
 | title = Nonsymmetric Theory of Gravitation
 | journal = Phys. Rev. D
 | volume = 56
 | issue = 2
 | pages = 864–873
 | date = 1997
 | author = S. Ragusa
 | doi = 10.1103/PhysRevD.56.864      |bibcode = 1997PhRvD..56..864R }}</ref><ref name=Janssen2007>{{Citation
 | title = Problems and hopes in nonsymmetric gravity
 | journal = J. Phys. A
 | date = 2007
 | volume = 40
 | issue = 25
 | pages = 7067–7074
 | last1 = Janssen   | first1 = T.
 | last2 = Prokopec  | first2 = T.
 | doi = 10.1088/1751-8113/40/25/S63  |bibcode = 2007JPhA...40.7067J | arxiv=gr-qc/0611005| s2cid = 6502419
 }}</ref>

In the weak field approximation where interaction between fields is not taken into account, NGT is characterized by a symmetric rank-2 tensor field (gravity), an antisymmetric tensor field, and a constant characterizing the mass of the antisymmetric tensor field. The antisymmetric tensor field is found to satisfy the equations of a [[Proca action|Maxwell–Proca]] massive antisymmetric tensor field. This led Moffat to propose [[metric-skew-tensor-gravity]] (MSTG),<ref name=Moffat2005>{{Citation
 | title = Gravitational Theory, Galaxy Rotation Curves and Cosmology without Dark Matter
 | author = J. W. Moffat
 | journal = Journal of Cosmology and Astroparticle Physics
 | volume = 2005
 | issue = 5
 | pages = 3
 | doi = 10.1088/1475-7516/2005/05/003
 | date = 2005 |bibcode = 2005JCAP...05..003M
 | arxiv=astro-ph/0412195| s2cid = 307531
 }}</ref> in which a skew symmetric tensor field postulated as part of the gravitational action.

A newer version of MSTG, in which the skew symmetric tensor field was replaced by a vector field, is [[scalar–tensor–vector gravity]] (STVG). STVG, like [[Mordehai Milgrom|Milgrom]]'s [[Modified Newtonian Dynamics]] (MOND), can provide an explanation for flat rotation curves of galaxies.

In 2013, Hammond showed the nonsymmetric part of the metric tensor was shown to be equal to the torsion potential, a result following the metricity condition, that the length of a vector is invariant under parallel transport. In addition, the energy momentum tensor is not symmetric, and both the symmetric and nonsymmetric parts are those of a string.<ref name=Hammond>{{Citation
 | title = Spin from the Nonsymmetric Metric Tensor
 | journal = International Journal of Modern Physics D
 | date = 2013
 | volume = 22
 | issue = 12
 | pages = 1342009
 | author = Richard T. Hammond
 | doi=10.1142/s0218271813420091
 | bibcode = 2013IJMPD..2242009H
 }}</ref>

== See also ==

* [[Reinventing Gravity]]

==References==
{{Reflist}}

{{theories of gravitation}}

{{DEFAULTSORT:Nonsymmetric Gravitational Theory}}
[[Category:Theories of gravity]]