An Alternative Variational Principle for Geodesics of a Randers Metric

Abstract

Abstract We present an alternative variational principle for the geodesics of a Randers metric. We define a functional I on the manifold of H1,2 curves joining two points on a Randers manifold (M, F) defined by a Riemannian metric g and a differential form ω. The functional I is of class C2, so it is more regular than the usual action functional, which is only of class C1,1. Moreover the critical points of the functional I are the geodesics for the Randers metric F reparameterized with Riemannian length g constant. Some global properties of the functional I are investigated. Finally some applications to the Fermat principle in stationary spacetimes will be presented.