Nonsymmetric gravitational theory
Encyclopedia
In theoretical physics
, the nonsymmetric gravitational theory (NGT) of John Moffat is a classical
theory of gravitation
which tries to explain the observation of the flat rotation curves of galaxies
.
In general relativity
, the gravitational field is characterized by a symmetric rank-2 tensor
, the metric tensor
. The possibility of generalizing the metric tensor has been considered by many, including Einstein 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
: 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 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.
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, the nonsymmetric gravitational theory (NGT) of John Moffat is a classical
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
theory of gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
which tries to explain the observation of the flat rotation curves of galaxies
Galaxy rotation curve
The rotation curve of a galaxy can be represented by a graph that plots the orbital velocity of the stars or gas in the galaxy on the y-axis against the distance from the center of the galaxy on the x-axis....
.
In general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, the gravitational field is characterized by a symmetric rank-2 tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...
, the metric tensor
Metric tensor
In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold which takes as input a pair of tangent vectors v and w and produces a real number g in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean...
. The possibility of generalizing the metric tensor has been considered by many, including Einstein and others. A general (nonsymmetric) tensor can always be decomposed into a symmetric and an antisymmetric part. As the electromagnetic field
Electromagnetic field
An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...
is characterized by an antisymmetric rank-2 tensor, there is an obvious possibility for a unified theory
Unified field theory
In physics, a unified field theory, occasionally referred to as a uniform field theory, 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 single field. There is no accepted unified field theory, and thus...
: 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 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
Proca action
In physics, in the area of field theory, the Proca action describes a massive spin-1 field of mass m in Minkowski spacetime. The field involved is a real vector field A...
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
Scalar-tensor-vector gravity
Scalar–tensor–vector gravity is a modified theory of gravity developed by John Moffat, a researcher at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario...
(STVG). STVG, like Milgrom
Mordehai Milgrom
Mordehai Milgrom is an Israeli physicist and professor in the department of Condensed Matter Physics at the Weizmann Institute in Rehovot, Israel. He is most famous for his proposal of Modified Newtonian dynamics as an alternative to the dark matter and galaxy rotation curve problems, in 1981...
's Modified Newtonian Dynamics
Modified Newtonian dynamics
In physics, Modified Newtonian dynamics is a hypothesis that proposes a modification of Newton's law of gravity to explain the galaxy rotation problem. When the uniform velocity of rotation of galaxies was first observed, it was unexpected because Newtonian theory of gravity predicts that objects...
(MOND), can provide an explanation for flat rotation curves of galaxies.