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Multiple periodic trajectories on stationary space-times. (English) Zbl 0777.53066

Verf. betrachtet zeitartige Geodäten \(\vec x=\vec x(s)\), \(t=t(s)\) in einer stationären Raum-Zeit mit der Eigenschaft \(\vec x(s+1)=\vec x(s)\), \(t(s+1)=t(s)+T\) \((T>0)\) und beweist, daß es unter passenden Annahmen über die Metrik (u.a., daß die Raum-Zeit im räumlich Unendlichen flach ist) zu jeder natürlichen Zahl \(n\) ein \(T_ 0>0\) derart gibt, daß für \(T\geq T_ 0n\) nichttriviale (und geometrisch sich unterscheidende) Geodäten dieser Art existieren.

MSC:

53Z05 Applications of differential geometry to physics
83C10 Equations of motion in general relativity and gravitational theory
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