Remarks on gravitational interaction in Kaluza-Klein models

Abstract

In these remarks, we clarify the problematic aspects of gravitational interaction in a weak-field limit of Kaluza-Klein models. We explain why some models meet the classical gravitational tests, while others do not. We show that variation of the total volume of the internal spaces generates the fifth force. This is the main reason of the problem. It happens for all considered models (linear with respect to the scalar curvature and nonlinear $f(R)$, with toroidal and spherical compactifications). We explicitly single out the contribution of the fifth force to nonrelativistic gravitational potentials. In the case of models with toroidal compactification, we demonstrate how tension (with and without effects of nonlinearity) of the gravitating source can fix the total volume of the internal space, resulting in the vanishing fifth force and consequently in agreement with the observations. It takes place for latent solitons, black strings and black branes. We also demonstrate a particular example where non-vanishing variations of the internal space volume do not contradict the gravitational experiments. In the case of spherical compactification, the fifth force is replaced by the Yukawa interaction for models with the stabilized internal space. For large Yukawa masses, the effect of this interaction is negligibly small, and considered models satisfy the gravitational tests at the same level of accuracy as general relativity.

13 pages, no figures. Reference and appendix added

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• Many-body problem in Kaluza-Klein models with toroidal compactification
• Exact and asymptotic black branes with spherical compactification
• Weak field limit of higher dimensional massive Brans-Dicke gravity: Observational constraints
• Weak-field limit of Kaluza-Klein model with non-linear perfect fluid
• Weak-field limit of Kaluza-Klein models with spherically symmetric static scalar field: observational constraints
• Effects of nonlinearity of $f(R)$ gravity and perfect fluid in Kaluza-Klein models with spherical compactification