Gravitational acceleration in Minkowski space (Q913285)

A reference frame is described using a time-like congruence K for which a corresponding canonical co-moving system of four-dimensional coordinates is introduced. Then the time coordinate is interpreted as the proper global time on the world lines K, while \(g_{\alpha 4}=u_{\alpha}\) \((\alpha =1,2,3\); \(u_{\alpha}\) being the four-velocity covector). Finally, a local relation between the Newtonian acceleration and the relativistic one, is established, which has in general a non-holonomic nature.