On the existence of geodesics on stationary Lorentz manifolds with convex boundary

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Abstract

In this paper we consider the problem of the existence and multiplicity for geodesics not touching the boundary of a stationary Lorentz manifold having convex boundary. A physical example of a stationary (and nonstatic) Lorentz manifold having convex boundary is the stationary, axisymmetric, asymptotically flat, gravitational field outside a rotating massive object, whenever its angular speed is small and its mean radius is close to the Schwarzschild radius.

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Sponsored by M.U.R.S.T. (Research funds 60% and 40%).