International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 11, Pages 86952, 16 p.
doi:10.1155/IJMMS/2006/86952

Timelike trajectories with fixed energy under a potential in static spacetimes

Abstract

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.