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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).
L −2 M −1 T 3 I 2: scalar Electrical conductivity: σ: Measure of a material's ability to conduct an electric current S/m L −3 M −1 T 3 I 2: scalar Electric potential: φ: Energy required to move a unit charge through an electric field from a reference point volt (V = J/C) L 2 M T −3 I −1: extensive, scalar Electrical resistance: R
The final main class of metric theories is the vector–tensor theories. For all of these the gravitational "constant" varies with time and α 2 {\displaystyle \alpha _{2}} is non-zero. Lunar laser ranging experiments tightly constrain the variation of the gravitational "constant" with time and α 2 < 4 × 10 − 7 {\displaystyle \alpha _{2}<4 ...
It has dimension of square reciprocal time, in units of s −2 (or m ⋅ m −1 ⋅ s −2). Gravity gradiometry is used by oil and mineral prospectors to measure the density of the subsurface, effectively by measuring the rate of change of gravitational acceleration due to underlying rock properties. From this information it is possible to ...