Inhomogeneous multidimensional cosmologies

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.