Frame fields in general relativity

Summary

A frame field, also called a tetrad or vierbein, is a choice of four vector fields on a region of spacetime. At each point they form an orthonormal basis, with one timelike and three spacelike vectors. It models a family of observers, each carrying a clock and three orthogonal measuring rods. Components of tensors with respect to a frame field are the values that these observers actually measure. Frame fields are needed to describe spinor fields in curved spacetime and they underlie the Newman–Penrose and the Cartan formalisms.