Gordon Metric Revisited

TL;DR

This paper extends the Gordon metric framework, showing it as part of a broader class of geometries that can describe accelerated bodies in dielectrics as geodesics, enabling force elimination through metric changes.

Contribution

It introduces a generalized class of geometries that encompass the Gordon metric, allowing for a broader description of accelerated bodies as geodesics in modified metrics.

Findings

Gordon metric is part of a larger geometric class.

Bodies' accelerated paths can be described as geodesics in a modified metric.

Force effects can be eliminated via suitable metric transformations.

Abstract

We show that Gordon metric belongs to a larger class of geometries, which are responsible to describe the paths of accelerated bodies in moving dielectrics as geodesics in a metric $\hat q_{\mu\nu}$ different from the background one. This map depends only on the background metric and on the motion of the bodies under consideration. As a consequence, this method describes a more general property that concerns the elimination of any kind of force acting on bodies by a suitable change of the substratum metric.