No 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.Comment: 29 pages, accepted to GR

In the modern version of 5-D general relativity where the fifth dimension induces matter in 4-D space–time, a choice of coordinates and its restrictions on the geometry (a gauge) dictates the physics of the gravitational, electromagnetic, and scalar fields (spin 2, 1, 0). We extend previous work by concentrating on two related problems. First, we use the lapse and shift formalism to carry out a (4+1) split of Kaluza–Klein theory valid in any gauge. Second, we use a conformal gauge to simplify the 5-D field equations, find a plane-wave solution, and identify the energy and momentum of the particle associated with it.

We study the quantum cosmology of a five dimensional non-compactified KaluzaKlein theory where the 4D metric depends on the fifth coordinate, x 4 ≡ l. This model is effectively equivalent to a 4D non-minimally coupled dilaton field in addition to matter generated on hypersurfaces l = constant by the extra coordinate dependence in the fourdimensional metric. We show that the Vilenkin wave function of the universe is more convenient for this model as it predicts a new-born 4D universe on the l ≃ 0 constant hypersurface.

The energy of 5D Kaluza-Klein gravity is studied for two types of spacetimes. The first set does not have any extra-coordinate dependence and we make use of a conformal transformation to make contact with minimally and non-minimally coupled theories of gravity, as well as Brans-Dicke theory. The energy for these theories is derived from the action as well as from conserved quantities associated with Killing vectors for scalar-tensor theories. The second class of metrics have the extra-coordinate dependence concentrated in a conformal factor on the 4D part of the 5D metric and the energy associated with these spacetimes is shown to be equivalent to the Abbott-Deser energy for asymptotically de Sitter spacetimes. We make contact with previous definitions of energy considered in the literature and we explicitly calculate the energy and angular momentum of some stationary solutions in Kaluza-Klein and Brans-Dicke gravity.