  In this paper we consider the Kaluza-Klein fields equations in presence of a
generic 5D matter tensor which is governed by a conservation equation due to 5D
Bianchi identities. Following a previous work, we provide a consistent approach
to matter where the problem of huge massive modes is removed, without relaxing
the compactification hypotheses; therefore we perform the dimensional reduction
either for metric fields and for matter, thus identifying a pure 4D tensor
term, a 4D vector term and a scalar one. Hence we are able to write down a
consistent set of equations for the complete dynamics of matter and fields ;
with respect to the pure Einstein-Maxwell system we now have two additional
scalar field: the usual dilaton one plus a scalar source term. Some significant
scenarios involving these terms are discussed and perspectives for cosmological
applications are suggested.
