# Frame Fields in General Relativity

Frame Fields In General Relativity

In general relativity, a frame field (also called a tetrad or vierbein) is a set of four orthonormal vector fields, one timelike and three spacelike, defined on a Lorentzian manifold that is physically interpreted as a model of spacetime. The timelike unit vector field is often denoted by and the three spacelike unit vector fields by . All tensorial quantities defined on the manifold can be expressed using the frame field and its dual coframe field.

Frames were introduced into general relativity by Hermann Weyl in 1929.

The general theory of tetrads (and analogs in dimensions other than 4) is described in the article on Cartan formalism; the index notation for tetrads is explained in tetrad (index notation).

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