**Difficulty level:**★ ★ ★

The following is a natural choice of orthonormal tetrad for an observer moving radially in Schwarzschild spacetime with “energy per unit rest mass” *e*:

The components are given in Schwarzschild coordinates. (The ± signs are not independent — they must be either both +1 or both -1. Note that *e* does not distinguish between inward and outward motion. There is additional freedom to define any of these vectors as their negative.)

We normally think of *e* as invariant, where there is a presumption of freely falling / geodesic motion, but even if not we can regard it as an instantaneous value.

is the 4-velocity computed previously. The other vectors can be obtained from substituting and into the tetrad here. is determined from and the equation for *e* above, then *V* follows from inverting . This orthonormal frame is useful for determining the object’s perspective, e.g. tidal forces, visual appearances, etc.