PROBLEMATIC ASPECTS OF TOROIDAL AND SPHERICAL　COMPACTIFICATIONS OF EXTRA DIMENSIONS IN KALUZA-KLEIN GEOMETRIES

摘要

In our recent papers we have investigated linear (with respect to the scalar curvature) as well as non-linear f(R) Kaluza-Klein models with both toroidal and spherical compactifications of an arbitrary number of extra dimensions and non-dust-like matter sources of the gravitational field concerning compatibility with the experimental data (laboratory and astrophysical tests). In the case of toroidal extra dimensions only latent solitons (in particular, black strings and black branes), possessing relativistic negative tension, satisfy the observations. In the case of spherical compactification a dust-like matter source also satisfies them under certain conditions, iniposed on the parameters of the model. However, there is the other problematic aspect in this case. Together with the perturbation of the background matter, which provides the internal space curvature, the dust-like source looks like an effective source, which has the nondust-like equation of state in the external space. Again introducing tension, one can avoid this difficulty, but tension itself has no clear physical origin. Thus, this possibility is not satisfactory enough. We present a brief review of our results, which prejudice Kaluza-Klein models.