Concept of semi-velocity and related wave equation (1712.08495v1)

Abstract: The semi-velocity is defined as an exponential function of the rapidity. Physically the semi-velocity is interpreted as the relativistic analogue of the phase velocity, a geometrical interpretation done within the framework of Beltrami-Klein and Poincar\'e models. A kinematical wave equation related with the Fermat principle and the concept of the semi-velocity is derived.