Dragged Metrics

We show that the path of any accelerated body in an arbitrary space-time geometry $g_{\mu \nu }$ can be described as geodesics in a dragged metric ${\widehat{q}}_{\mu \nu }$ that depends only on the background metric and on the motion of the body. Such procedure allows the interpretation of all kind of non-gravitational forces as modifications of the metric of space-time. This method of effective elimination of the forces by a change of the metric of the substratum can be understood as a generalization of the d’Alembert principle applied to all relativistic processes.