Orthonormal tetrad transport. II. Physical identification of the normals and curvatures of a time-like curve

A flat space-time time-like curve is considered from the point of view of an instantaneous comoving inertial observer. In the context of the ‘vierbein’ formalism a projection operator is introduced, able to project 3-vectors, belonging to the 3-space of the comoving observer, out of space-time 4-vectors. The motion of an accelerated particle relative to the comoving inertial frame is briefly reviewed by means of the projection technique, and the three space-like components of the Frenet-Serret tetrad are thus projected, and their motion relative to the comoving observer neatly stated. Finally, the physical identification of the normals and the curvatures obtains in terms of three-dimensional kinematics as seen by the instantaneous comoving observer.