Abstract
Vacuum solutions in multidimensional Kaluza-Klein theories with arbitrary signature are considered. Solutions of 11- and 10-dimensional supergravity theories satisfying the criteria for the absence of ghosts in the effective massless four-dimensional theory are obtained. Solutions corresponding to two four-dimensional universes are constructed, and their possible cosmological consequences are discussed. For D = 10, N = 2 supergravity vacuum solutions with zero cosmological constant are obtained.
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