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 List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

, the nonsymmetric gravitational theory (NGT) of John Moffat is a classical theory of

gravitation In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...

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 as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...

, the gravitational field is characterized by a symmetric rank-2

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

, the

metric tensor In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows ...

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

Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...

and others. A general (nonsymmetric) tensor can always be decomposed into a symmetric and an antisymmetric part. As the

electromagnetic field An electromagnetic field (also EM field) is a physical field, varying in space and time, that represents the electric and magnetic influences generated by and acting upon electric charges. The field at any point in space and time can be regarde ...

is characterized by an antisymmetric rank-2 tensor, there is an obvious possibility for a unified theory: 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 via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

. 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 (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

See also

References