Geodesics of Deformed Relativity in Five Dimensions

摘要

In a previous paper, we discussed the Killing symmetries of the Kaluza-Klein-likescheme known as Deformed Relativity in five dimensions (DR5), based on a five-dimensionalRiemannian space 5 in which the four-dimensional space-time metric is deformed (i.e. itdepends on the energy) and energy plays the role of the fifth dimension. In the present paper,we carry on the investigation of the main mathematical aspects of DR5 by studying the geodesicmotions in 5. In particular, we consider the case of physical relevance in which the metriccoefficients are power functions of the energy (Power Ansatz). The geodesic equations are solvedexplicitly for all the twelve 5-d. metrics obtained as solutions of the vacuum Einstein equations,and in particular for those describing the four fundamental interactions. It is also shown thatit is possible, from the geodesic motion related to one of these Power-Ansatz solutions, to get atime-energy uncertainty relation of the Heisenberg type.