We state a fundamental correspondence between geodesics on stationary spacetimes and the equations of classical particles on Riemannian manifolds, accelerated by a potential and a magnetic field. By varia- tional methods, we prove some existence and multiplicity theorems for fixed energy solutions (joining two points or periodic) of the above described Riemannian equation. As a consequence, we obtain existence and multiplicity results for geodesics with fixed energy, connecting a point to a line or periodic trajectories, in (standard) stationary spacetimes.

Geodesics in stationary spacetimes and classical Lagrangian systems

GERMINARIO, Anna
2007-01-01

Abstract

We state a fundamental correspondence between geodesics on stationary spacetimes and the equations of classical particles on Riemannian manifolds, accelerated by a potential and a magnetic field. By varia- tional methods, we prove some existence and multiplicity theorems for fixed energy solutions (joining two points or periodic) of the above described Riemannian equation. As a consequence, we obtain existence and multiplicity results for geodesics with fixed energy, connecting a point to a line or periodic trajectories, in (standard) stationary spacetimes.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/48953
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