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Concept
Tensor–vector–scalar gravity
Résumé
Tensor–vector–scalar gravity (TeVeS), developed by Jacob Bekenstein in 2004, is a relativistic generalization of Mordehai Milgrom's Modified Newtonian dynamics (MOND) paradigm.
The main features of TeVeS can be summarized as follows:
As it is derived from the action principle, TeVeS respects conservation laws;
In the weak-field approximation of the spherically symmetric, static solution, TeVeS reproduces the MOND acceleration formula;
TeVeS avoids the problems of earlier attempts to generalize MOND, such as superluminal propagation;
As it is a relativistic theory it can accommodate gravitational lensing.
The theory is based on the following ingredients:
A unit vector field;
A dynamical scalar field;
A nondynamical scalar field;
A matter Lagrangian constructed using an alternate metric;
An arbitrary dimensionless function.
These components are combined into a relativistic Lagrangian density, which forms the basis of TeVeS theory.
MOND is a phenomenological modification of the Newtonian acceleration law. In Newtonian gravity theory, the gravitational acceleration in the spherically symmetric, static field of a point mass at distance from the source can be written as
where is Newton's constant of gravitation. The corresponding force acting on a test mass is
To account for the anomalous rotation curves of spiral galaxies, Milgrom proposed a modification of this force law in the form
where is an arbitrary function subject to the following conditions:
In this form, MOND is not a complete theory: for instance, it violates the law of momentum conservation.
However, such conservation laws are automatically satisfied for physical theories that are derived using an action principle. This led Bekenstein to a first, nonrelativistic generalization of MOND. This theory, called AQUAL (for A QUAdratic Lagrangian) is based on the Lagrangian
where is the Newtonian gravitational potential, is the mass density, and is a dimensionless function.
In the case of a spherically symmetric, static gravitational field, this Lagrangian reproduces the MOND acceleration law after the substitutions and are made.
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