Dragged Metrics

TL;DR

The paper demonstrates that any accelerated motion in a general space-time can be viewed as geodesic motion in a modified metric, effectively turning non-gravitational forces into geometric effects.

Contribution

It introduces a method to represent all non-gravitational forces as modifications of the space-time metric, generalizing the d'Alembert principle to relativistic contexts.

Findings

Any accelerated path can be described as a geodesic in a dragged metric.

Non-gravitational forces can be interpreted as metric modifications.

The approach generalizes classical principles to relativistic space-time.

Abstract

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 $\hat{q}_{\mu\nu}$ 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.