Asymmetric gravity theories

The asymmetric theory of gravity ^[1] (NTG) by John Moffat is a variant of the classical theory of gravity , which offers an explanation of the riddle of dark matter .

In the general theory of relativity, the gravitational field is characterized by a symmetric tensor of rank 2, known as the metric tensor . The possibility of generalizing the metric tensor was considered by many, including Einstein . In the general case (arbitrary asymmetric) tensor can always be decomposed into symmetric and antisymmetric parts. Since the electromagnetic field is characterized by an antisymmetric tensor of rank 2, there is an obvious opportunity to construct a unified theory in the form of an asymmetric tensor consisting of a symmetric part representing gravity and an antisymmetric part representing electromagnetism. Investigations in this direction ultimately proved unsuccessful - the desired classical unified field theory was not found.

In 1979, Moffat ^[2] noted that the antisymmetric part of the generalized metric tensor does not have to represent electromagnetism; it may be a kind of new hypothetical type of interaction. Later, in 1995, Moffat noted ^[1] that the field corresponding to the antisymmetric part does not have to be massless, as is the case with electromagnetic (and also gravitational) interaction.

In its original form, the theory may be unstable, although this has been shown only for the linearized version of the theory. ^{[3] [4]}

In the weak field approximation, when the interaction between the fields is not taken into account, the NTG is characterized by a symmetric tensor field of rank 2 (representing gravity), an antisymmetric tensor field, and a constant characterizing the mass of the antisymmetric tensor field. It was found that an antisymmetric tensor field should satisfy the Maxwell-Prock equations for a massive antisymmetric tensor field. This led Moffat to the proposal of the Metric-Kososymmetric-Tensor Gravity Theory ( Metric Skew Tensor Gravity ) (MSTG), ^[5] in which the skew-symmetric tensor field is postulated as part of the gravitational action.

The new version of MSTG, in which the skew-symmetric tensor field was replaced by a vector field, is called Scalar-Tensor-Vector Theory of Gravity (English) ( Scalar-tensor-vector gravity ) (STVG). STVG, like the Modified Newtonian Dynamics (MOND) by Mordechai Milgrom , offers the option of explaining the observed flat curves of the rotation of galaxies .