Observational constraints on Kaluza-Klein models with $d$-dimensional spherical compactification

TL;DR

This paper explores Kaluza-Klein models with spherical internal space compactification, analyzing metric perturbations and showing that Yukawa interactions can be suppressed in the Solar system, with effective pressures depending on internal space tension.

Contribution

It provides a detailed analysis of metric perturbations in higher-dimensional Kaluza-Klein models with arbitrary internal space equations of state, including conditions for internal space stabilization.

Findings

Yukawa interaction effects depend on internal space stabilization conditions.

In the Solar system, Yukawa effects are negligible for all internal space equations of state.

Effective relativistic pressure in external space depends on internal space tension, vanishing at /2 tension.

Abstract

We investigate Kaluza-Klein models in the case of spherical compactification of the internal space with an arbitrary number of dimensions. The gravitating source has the dust-like equation of state in the external/our space and an arbitrary equation of state (with the parameter $\Omega$) in the internal space. We get the perturbed (up to $O(1/c^2)$) metric coefficients. For the external space, these coefficients consist of two parts: the standard general relativity expressions plus the admixture of the Yukawa interaction. This admixture takes place only for some certain condition which is equivalent to the condition for the internal space stabilization. We demonstrate that the mass of the Yukawa interaction is defined by the mass of the gravexciton/radion. In the Solar system, the Yukawa mass is big enough for dropping the admixture of this interaction and getting good agreement with the gravitational tests for any value of $\Omega$. However, the gravitating body acquires the effective relativistic pressure in the external space which vanishes only in the case of tension $\Omega=-1/2$ in the internal space.