Tensor–vector–scalar gravity (TeVeS), developed by Jacob Bekenstein

Jacob Bekenstein

Jacob David Bekenstein is an Israeli theoretical physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation.-Biography:...

, is a relativistic generalization of Mordehai 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) 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.

The theory is based on the following ingredients:

• A unit vector field
  Vector field
  In vector calculus, a vector field is an assignmentof a vector to each point in a subset of Euclidean space. A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane...
  
  ;
• A dynamical scalar field
  Scalar field
  In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the...
  
  ;
• A nondynamical scalar field;
• A matter Lagrangian
  Lagrangian
  The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...
  
   constructed using an alternate metric
  Metric (mathematics)
  In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a 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.