The qualitative theory of dynamical systems is used to present an analysis of the phase space of Kaluza-Klein cosmological solutions with even-dimensional internal space, an arbitrary cosmological constant, and Freund-Rubin compactification. If either the physical or internal manifold has a single spatial dimension the cosmological solutions may correspond to black-hole interiors and pathological behavior can be expected. It is shown that such behavior does not occur in general, however. Some solutions with dilatons are also discussed.
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David L. Wiltshire (1987) studied this question.
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