Cosmological implications of a nonseparable 5D solution of the vacuum Einstein field equations

An exact class of solutions of the 5D vacuum Einstein field equations (EFEs ) is obtained. The metric coefficients are found to be nonseparable functio ns of time and the extra coordinate l and the induced metric on l=const hyp ersurfaces has the form of a Friedmann-Robertson-Walker cosmology. The 5D m anifold and 3D and 4D submanifolds are in general curved, which distinguish es this solution from previous ones in the literature. The singularity stru cture of the manifold is explored: some models in the class do not exhibit a big bang, while others exhibit a big bang and a big crunch. For the model s with an initial singularity, the equation of state of the induced matter evolves from radiation-like at early epochs to Milne-like at late times and the big bang manifests itself as a singular hypersurface in 5D. The projec tion of comoving 5D null geodesics onto the 4D submanifold is shown to be c ompatible with standard 4D comoving trajectories, while the expansion of 5D null congruences is shown to be in line with conventional notions of the H ubble expansion. (C) 2001 American Institute of Physics.