Relativity and Rotation

Summary

Introduction

It was an honour to be a student of Charles Misner. And it was a pleasure to work with him. It is once again an honour and a pleasure to write an article in celebration of his sixtieth birthday.

The phenomenon of rotation generates interesting physical effects and involves intriguing basic concepts. One of the earliest classic examples of this is Newton's water-pail experiment. Within the framework of the general theory of relativity rotation displays rather unusual features. These are incorporated, for instance, in the spacetime structure such as that of a rotating black hole. Dragging of inertial frames and the occurrence of the ergosphere, to name two examples, are the outcome of the rotation built into the spacetime. Rotational effects also show up in the characteristics of particle motion and associated phenomena like gyroscope precession. These effects are revealed in an elegant manner by the invariant geometrical description of particle trajectories following the directions of spacetime symmetries, assuming that the spacetime under consideration admits such symmetries. In three dimensions, this geometrical characterization involves the specification of the curvature κ and torsion τ of the curve as functions of some parameter that varies along the curve, normally the arc-length. This can be extended to higher dimensions including time and the relevant geometrical parameters would then be κ, τ₁, τ₂…τ_n-1 for n-dimensions. These parameters fit naturally into the Frenet-Serret formalism that is well known to the geometers. When the formalism is applied to timelike integral curves of space symmetries many interesting features emerge. In the major part of this article we shall briefly review the results that have been obtained in this area of investigation.