Einstein's equations for a (4 + n)-dimensional inhomogeneous space-time are
presented, and a special family of solutions is exhibited for an arbitrary
n. The solutions depend on two arbitrary functions of time. The time devel
opment of a particular member of this family is studied. This solution exhi
bits a singularity at t = 0 and dynamical compactification of the n dimensi
ons. It is shown that the behavior of the system in the four-dimensional (i
.e. post-compactification) phase is constrained by the way in which the com
pactified dimensions are stabilized. The fluid that generates this solution
is analyzed by means of the energy conditions.