theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

, the nonsymmetric gravitational theory (NGT) of John Moffat is a classical theory of gravitation that tries to explain the observation of the flat rotation curves of galaxies. In

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

, the gravitational field is characterized by a

symmetric Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...

rank-2

tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...

, the metric tensor. The possibility of generalizing the metric tensor has been considered by many, including

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...

and others. A general (nonsymmetric) tensor can always be decomposed into a symmetric and an antisymmetric part. As the electromagnetic field is characterized by an antisymmetric rank-2 tensor, there is an obvious possibility for a

unified theory In physics, a unified field theory (UFT) is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a pair of physical and virtual fields. According to the modern ...

: a nonsymmetric tensor composed of a symmetric part representing gravity, and an antisymmetric part that represents

electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...

. Research in this direction ultimately proved fruitless; the desired classical unified field theory was not found. In 1979, Moffat made the observation 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 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. 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 Maxwell–Proca massive antisymmetric tensor field. This led Moffat to propose metric-skew-tensor-gravity (MSTG), 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 Milgrom's

Modified Newtonian Dynamics Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaining ...

(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.

References

{{DEFAULTSORT:Nonsymmetric Gravitational Theory Theories of gravity