ABSTRACT
One of the first variational principles proved in Physics was the Fermat principle for light rays. A light ray which connects two points in the space chooses a trajectory which makes stationary the arrival time. A similar variational principle holds in General Relativity. Consider an event of a space-time and a timelike curve, then the light rays joining the event with the timelike curve make stationary the arrival time, defined in a subtle way (see [Pr1] for a general proof of this principle and for historical references). In [U] a Morse Theory for the light rays joining an event with a given timelike curve is developed in a global hyperbolic Lorentzian manifold with some restriction on the metric at infinity.
