Four-acceleration is a concept from the framework of special relativity and general relativity that describes the change in four-velocity of an object with respect to proper time. It serves as a relativistic generalization of classical acceleration. ### Definition: Four-acceleration, denoted often as \( A^\mu \), is defined as the derivative of the four-velocity \( U^\mu \) with respect to the proper time \( \tau \).
Articles by others on the same topic
The four-acceleration is the covariant derivative of four-velocity along a massive observer's worldline: . In Cartesian Minkowski spacetime coordinates the Christoffel symbols vanish, leaving the ordinary proper time derivative. Differentiating the constant velocity norm gives ; in the instantaneous rest frame, , so with metric signature. The magnitude is the proper acceleration.