Frame fields in general relativity

In general relativity, a frame field (also called a tetrad or vierbein) is a set of four pointwise-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 e → 0 {\displaystyle {\vec {e}}_{0}} and the three spacelike unit vector fields by e → 1 , e → 2 , e → 3 {\displaystyle {\vec {e}}_{1},{\vec {e}}_{2},\,{\vec {e}}_{3}} .

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