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Lightlike periodic trajectories in space-times

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Let 〈., 〉z be a Lorentz metric on a manifold \(\mathfrak{M} = \mathfrak{M}_0 \times R\) such that \(\mathfrak{M}_0 \) isnot compact. We prove the existence of infinitely many lightlike periodic trajectories in \(\mathfrak{M}\) by using variational methods and Ljusternik-Schnirelman theory.


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Sponsored by M.U.R.S.T. (fondi 60% «Problemi differenziali nonlineari e teoria dei punti critici»; fondi 40% «Equazioni differenziali e calcolo delle variazioni»).

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Candela, A.M. Lightlike periodic trajectories in space-times. Annali di Matematica pura ed applicata 171, 131–158 (1996).

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  • Variational Method
  • Periodic Trajectory