On the accelerated observer's proper coordinates and the rigid motion problem in Minkowski spacetime

TL;DR

This paper develops a systematic method to define rigid motion for accelerated observers in Minkowski spacetime by expressing the metric through Frenet-Serret curvatures and proper coordinates, with applications to Rindler, rotating, and cylindrical observers.

Contribution

It introduces a new approach to construct rigid motions for accelerated observers using Frenet-Serret curvatures and proper coordinates in Minkowski spacetime.

Findings

Systematic construction of rigid motions for accelerated observers.

Application to Rindler and rotating observers.

Proposal of a rigid cylindrical observer model.

Abstract

Physicists have been interested in accelerated observers for quite some time. Since the advent of special relativity, many authors have tried to understand these observers in the framework of Minkowski spacetime. One of the most important issues related to these observers is the problematic definition of rigid motion. In this paper, I write the metric in terms of the Frenet-Serret curvatures and the proper coordinate system of a general accelerated observer. Then, I use this approach to create a systematic way to construct a rigid motion in Minkowski spacetime. Finally, I exemplify the benefits of this procedure by applying it to two well-known observers, namely, the Rindler and the rotating ones, and also by creating a set of observers that, perhaps, may be interpreted as a rigid cylinder which rotates while accelerating along the axis of rotation.