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 development of a particular member of this family is studied. This solution exhibits a singularity at t = 0 and dynamical compactification of the n dimensions. 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 compactified dimensions are stabilized. The fluid that generates this solution is analyzed by means of the energy conditions.