Uniform circular motion in general relativity: existence and extendibility of the trajectories

Abstract

The concept of uniform circular motion in a general spacetime is introduced as a particular case of a planar motion. The initial value problem of the corresponding differential equation is analysed in detail. Geometrically, an observer that obeys a uniform circular motion is characterized as a Lorentzian helix. The completeness of inextensible trajectories is studied in generalized Robertson–Walker spacetimes and in a relevant family of pp-wave spacetimes. Under reasonable assumptions, the physical interpretation of such results is that a uniform circular observer lives forever, providing the absence of the singularities defined by these timelike curves.