Note on the displacement of a trajectory of hyperbolic motion in curved space-time
Collège de France - Institut d’Astrophysique de Paris - UMR7095 CNRS, Université Pierre et Marie Curie, 98bis boulevard Arago, 75014, Paris, France
Accepted: 19 March 2012
Published online: 9 April 2012
The object of this note is to present a physical application of the theory of the infinitesimal deformations or displacements of curves developed by Yano using the concept of Lie derivative. It is shown that an infinitesimal point transformation which carries a given trajectory of hyperbolic motion into a trajectory of the same type, and preserves the affine parametrization of the trajectory, defines a homothetic motion.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2012