SIGNIFICANCE OF TENSION FOR KALUZA-KLEIN MODELS: CRITICAL REMARKS - Eingorn, M. (Одеські астрономічні публікації, 2012)
In this very brief review the crucial problematic aspects of gravitational interaction in the weak field limit of Kaluza-Klein models are clarified. We explain why some models meet the classical gravitational tests, while the others do not. In the case of toroidal compactification of extra spatial dimensions we show how the presence of tension (both with and without effects of nonlinearity with respect to the scalar curvature R ) of a single gravitating source results in agreement with the observations. It takes place for so-called latent solitons, in particular, black strings and black branes. In the case of spherical compactification there is the additional (with respect to the Newtonian one) Yukawa interaction for models with the stabilized internal space. For large Yukawa masses the effect of this interaction is negligibly small, and such models satisfy the gravitational tests at the same level of accuracy as general relativity. However, gravitating masses acquire effective relativistic pressure in the external space. Obviously, such pressure contradicts the observations. We demonstrate that tension is the only possibility to preserve the dust-like equation of state in the external space. Therefore, tension plays a crucial role for multidimensional models.