Abstract.
We show that a static Lorentzian manifold satisfying a completeness assumption is geodesically connected. In particular, such condition is satisfied by all compact static manifolds; in the compact case, we also prove the existence of a closed geodesic in every free homotopy class determined by a finite number of deck transformations.
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Received: 28 July 2002 / Published online: 16 May 2003
Mathematics Subject Classification (1991): 53C22, 53C50, 58E10
The first and the second author are sponsored by the MIUR national project ``Metodi variazionali e topologici nello studio di fenomeni nonlineari''. The third author is partially sponsored by CNPq, Brazil.
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Caponio, E., Masiello, A. & Piccione, P. Some global properties of static spacetimes. Math. Z. 244, 457–468 (2003). https://doi.org/10.1007/s00209-003-0488-0
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DOI: https://doi.org/10.1007/s00209-003-0488-0