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

TL;DR

This paper explores how five-dimensional Kaluza-Klein gravity models can produce diverse four-dimensional physical phenomena, including variable particle masses and different interpretations of energy-momentum, depending on the metric and trajectory assumptions.

Contribution

It introduces a generalized approach to 5D metrics with extra coordinate dependence, revealing new physical implications and interpretations in induced matter scenarios.

Findings

5D null trajectories can correspond to massive or null 4D paths.

Variable particle masses can arise from extra-dimensional effects.

Late-time behavior allows particles to be consistent with induced matter models.

Abstract

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.