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.

Weak-field limit of Kaluza–Klein models with spherically symmetric static scalar field: observational constraints

“…This value is well known for black strings and black branes [9][10][11][12][13][14]. For KK models with Ricci-flat internal spaces, this result does not depend on the size of the extra dimensions [15]. 1 Since up to now there is no a physically motivated explanation of the origin of such an essentially non-zero value of the parameter Ω, we are asking about the possibility of constructing the KK models, for which, on the one hand, the PPN parameter γ will satisfy the experimental constraints (i.e.…”

Many-body problem in Kaluza–Klein models with toroidal compactification

“…As we have shown above [25][26][27], the tension in the internal spaces is the necessary condition to satisfy the gravitational experiments in KK models with toroidal compactification. In our paper, we have proven that the presence of pressure/tension in the internal space necessarily leads to the uniform smearing of the gravitating masses over the internal space.…”

“…This conclusion does not depend on the size of the extra dimensions. The physical reason of it is that in the case of toroidal compactification, only in the case of latent solitons the variations of the total volume of the internal space are absent [27].…”

Exact and asymptotic black branes with spherical compactification

“…In the weakfield limit, we have shown that a pointlike mass with the dustlike equation of state can satisfy the gravitational experiments if the model contains a positive cosmological constant [1]. It happens if the Yukawa interaction, generated by the conformal variations of the volume of the internal space [12], becomes negligible and we can drop the admixture of such interaction to the metric perturbations h 00 and h αα , α = 1, 2, 3, resulting in equality of h 00 and h αα . A natural question arises whether this approach is the only way to satisfy the gravitational experiments in the case of spherical compactification?…”