Abstract
In the literature concerned with the relativistic dynamics of a mass-point, the problem of finding geodesies is stated as a variational problem, and the equations for the geodesies are the Euler equations associated with it. This article discusses the case of geodesies of null-length in the Riemannian space-time of General Relativity, as they play an important role, in particular in connection with the hypothetic motion of photons in a gravitational field. It is shown that this problem is not in general a variational problem, but a problem of controllability.
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