4D induced matter from non-compact 5D Kaluza-Klein gravity

Abstract

The traditional constraints associated with five-dimensional Kaluza-Klein gravity are removed, namely that the 5D metric can depend on the extra-coordinate and that this coordinate is non-compact. The assumption that the 5D theory is vacuum RAB=0 is the minimal set of field equations to induce matter from 5D to 4D via a dimensional reduction. This reduction is carried out for two general types of 5D metrics: 1) the traditional Kaluza-Klein metric which unifies gravity, electromagnetism and a scalar field, and 2) conformal extra-coordinate dependent metric which induve an effective cosmological constant and realistic neutral matter. The physical aspects such as test particle motion, the weak-field limit and gravitational waves, and the energy from a Hamiltonian perspective and conserved quantities associated with scalar-tensor theories of gravity are studied in detail. It i found that 5D relativity is a rich extension of 4D gravity that unifies geometry with 4D matter.