International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 86952, 16 pages

Timelike trajectories with fixed energy under a potential in static spacetimes

Anna Germinario

Dipartimento di Matematica, Università degli Studi di Bari, Via E. Orabona 4, Bari 70125, Italy

Received 14 September 2005; Revised 26 May 2006; Accepted 30 May 2006

Copyright © 2006 Anna Germinario. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By variational methods, we study the motions of a relativistic particle under the action of an external scalar potential. We consider standard static spacetimes whose metric coefficients grow at most quadratically at infinity. Fixing suitable values for the energy, we obtain timelike trajectories.