Remarks on gravitational interaction in Kaluza-Klein models

TL;DR

This paper examines the gravitational interaction issues in Kaluza-Klein models, identifying the role of internal space volume variation and proposing conditions under which these models align with classical gravitational tests.

Contribution

It clarifies the problematic aspects of gravity in Kaluza-Klein models and shows how tension and internal space stabilization can eliminate the fifth force, improving model viability.

Findings

Variation of internal space volume causes the fifth force.

Tension in sources can fix internal volume, removing the fifth force.

Spherical compactification with stabilized internal space satisfies gravitational tests.

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.