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Scalar–tensor–vector gravity (STVG) [1] is a modified theory of gravity developed by John Moffat, a researcher at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario. The theory is also often referred to by the acronym MOG ( MO dified G ravity ).
An action of such a gravitational scalar–tensor theory can be written as follows: = [() () + (,)], where is the metric determinant, is the Ricci scalar constructed from the metric , is a coupling constant with the dimensions , () is the scalar-field potential, is the material Lagrangian and represents the non-gravitational fields.
Indeed, the theory he finally arrived at in 1915, general relativity, is a tensor theory, not a scalar theory, with a 2-tensor, the metric, as the potential. Unlike his 1913 scalar theory, it is generally covariant, and it does take into account the field energy–momentum–stress of the electromagnetic field (or any other nongravitational field).
Tensor–vector–scalar gravity (TeVeS), [1] developed by Jacob Bekenstein in 2004, is a relativistic generalization of Mordehai Milgrom's Modified Newtonian dynamics (MOND) paradigm. [2] [3] The main features of TeVeS can be summarized as follows: As it is derived from the action principle, TeVeS respects conservation laws;
This led Moffat to propose metric-skew-tensor-gravity (MSTG), [5] 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).
Moffat is best known for his work on gravity and cosmology, culminating in his nonsymmetric gravitational theory and scalar–tensor–vector gravity (now called MOG), and summarized in his 2008 book for general readers, Reinventing Gravity. His theory explains galactic rotation curves without invoking dark matter.
In physics, the Brans–Dicke theory of gravitation (sometimes called the Jordan–Brans–Dicke theory) is a competitor to Einstein's general theory of relativity.It is an example of a scalar–tensor theory, a gravitational theory in which the gravitational interaction is mediated by a scalar field as well as the tensor field of general relativity.
The Lagrangian in scalar-tensor theory can be expressed in the Jordan frame or in the Einstein frame, which are field variables that stress different aspects of the gravitational field equations and the evolution equations of the matter fields.