Ormal basis in schwarzschild coordinates consider the metric component o," o,= η"--1. if the observer is at rest in schwarzschild coordinates, then the spatial schwarzschild components of o,- ub must all be zero. therefore, (12.24) where gyw is the schwarzschild metric here. since the other components are zero, this leads to the first of equations 12.10. because this vector has no spatial components, the condition implies that o, has zero schwarzschild time component. the same argument ap- plies to the other spatial basis vectors. (note that if the observer were moving in schwarzschild spacetime, then o, would have nonzero spatial components, and the spatial basis vectors would possibly have a nonzero time component.) exercise 12.6.1. argue in the space provided on the next page that the rest of equations 12.10 are correct if ono,, and o, point in the φ,-9, and r directions, respectively, in schwarzschild spacetime.