en.wikipedia.org/wiki/Why_10_dimensions%3F
Space-time-matter theory
One particular variant of Kaluza–Klein theory is space-time-matter theory or
induced matter theory, chiefly promulgated by Paul Wesson and other members of
the so-called Space-Time-Matter Consortium. In this version of the theory, it is
noted that solutions to the equation
RAB = 0
with RAB the five-dimensional Ricci curvature, may be re-expressed so that in
four dimensions, these solutions satisfy Einstein's equations
Gμν = 8πTμν
with the precise form of the Tμν following from the Ricci-flat condition on the
five-dimensional space. Since the energy-momentum tensor Tμν 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 RAB = 0 can be shown to contain the
Robertson-Walker metric in both matter-dominated (early universe) and
radiation-dominated (present 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 models.
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