Uniform circular motion in General Relativity: Existence and extendibility of the trajectories

Abstract

The notion 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 di erential equation is analysed in detail. Geometrically, an observer which obeys a uniform circular motion is characterized as a Lorentzian helix. The completeness of its inextensible trajectories is studied in Generalized Robertson-Walker spacetimes and in a relevant family of pp-wave spacetimes. The results may be physically interpreted saying that, under reasonable assumptions, a uniformly circular observer lives forever in these spacetimes, providing the absence of the singularities de ned by these timelike curves.