Induced Matter and Particle Motion in Non-Compact Kaluza-Klein Gravity

We examine generalizations of the five–dimensional canonical metric by including a dependence of the extra coordinate in the four–dimensional metric. We discuss a more appropriate way to interpret the four–dimensional energy–momentum tensor induced from the five–dimensional space-time and show it can lead to quite different physical situations depending on the interpretation chosen. Furthermore, we show that the assumption of five–dimensional null trajectories in Kaluza–Klein gravity can correspond to either four–dimensional massive or null trajectories when the path parameterization is chosen properly. Retaining the extra–coordinate dependence in the metric, we show the possibility of a cosmological variation in the rest masses of particles and a consequent departure from four–dimensional geodesic motion by a geometric force. In the examples given, we show that at late times it is possible for particles traveling along 5D null geodesics to be in a frame consistent with the induced matter scenario.