Mathematics – Logic
Scientific paper
Aug 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989acppb..20..671s&link_type=abstract
Acta Phys. Pol., Ser. B, Vol. 20, No. 8, p. 671 - 700
Mathematics
Logic
1
Cosmological Models
Scientific paper
Thermodynamical functions are determined for the bosonic gas distribution in the external gravitational field described by multidimensional cosmological models having the structure FRW×BD, where BD is any D-dimensional compact space with the scalar curvature R(D). Universal asymptotics of this function are found for two situations. The results are applied to discuss the dimensional reduction generated by the classical Einstein equations with quantum corrections. It is demonstrated that, in the low-temperature approximation, there is no effective mechanism of the dimensional reduction to a static internal space, if BD is a group manifold. On the other hand, the effective mechanism of the dimensional reduction to the zero size does exist. The existence of such mechanism for the full class of multidimensional homogeneous cosmologies with the hydrodynamic energy-momentum tensor is also discussed.
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