An existence theory for relativistic brachistochrones in stationary space–times

Abstract

We use a variational principle proven by Giannoni et al. [J. Math. Phys. 38, 6367–6381 (1997)] for relativistic brachistochrones and techniques of global analysis to develop an existence theory for brachistochrones in stationary space–times. We also develop a Ljusternik–Schnirelman theory for brachistochrones, obtaining multiplicity results depending on the topology of the space–time.