Tensor–vector–scalar gravity

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.