Editing Kaluza–Klein theory (section)

== Space–time–matter theory ==
One particular variant of Kaluza–Klein theory is '''space–time–matter theory''' or '''induced matter theory''', chiefly promulgated by [[Paul S. Wesson|Paul Wesson]] and other members of the Space–Time–Matter Consortium.<ref>[http://5dstm.org 5Dstm.org]</ref> In this version of the theory, it is noted that solutions to the equation
: <math>\widetilde{R}_{ab}=0</math>
may be re-expressed so that in four dimensions, these solutions satisfy [[Einstein's equation]]s
: <math>G_{\mu\nu} = 8\pi T_{\mu\nu}\,</math>
with the precise form of the ''T''<sub>''μν''</sub> following from the [[Ricci-flat condition]] on the five-dimensional space. In other words, the cylinder condition of the previous development is dropped, and the stress–energy now comes from the derivatives of the 5D metric with respect to the fifth coordinate. Because the [[energy–momentum tensor]] is normally understood to be due to concentrations of matter in four-dimensional space, the above result is interpreted as saying that four-dimensional matter is induced from geometry in five-dimensional space.

In particular, the [[soliton]] solutions of <math>\widetilde{R}_{ab}=0</math> can be shown to contain the [[Friedmann–Lemaître–Robertson–Walker metric]] in both radiation-dominated (early universe) and matter-dominated (later universe) forms.  The general equations can be shown to be sufficiently consistent with classical [[tests of general relativity]] to be acceptable on physical principles, while still leaving considerable freedom to also provide interesting [[cosmological model]]s.