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 ${\displaystyle {\vec {e}}_{0}}$ and the three spacelike unit vector fields by ${\displaystyle {\vec {e}}_{1},{\vec {e}}_{2},\,{\vec {e}}_{3}}$. All tensorial quantities defined on the manifold can be expressed using the frame field and its dual coframe field.

...
Wikipedia