Summary
Let (R 4, g) be a spacetime manifold with a stationary Lorentz tensor g. We consider the problem of the existence of time like geodesic z(s)=(t(s), x(s)) on (R 4, g) with the periodicity conditions x(s+1)=x(s), t(s+1)=t(s)+T (T > 0). In this paper we prove, under suitable assumptions on g, multiplicity result for such a problem.
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Greco, C. Multiple periodic trajectories on stationary space-times. Annali di Matematica pura ed applicata 162, 337–348 (1992). https://doi.org/10.1007/BF01760014
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DOI: https://doi.org/10.1007/BF01760014