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

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.

💡 Research Summary

The paper investigates a class of Kaluza‑Klein (KK) models in which the extra dimensions are compactified on a d‑dimensional sphere of radius a, while the observable universe remains a four‑dimensional (3 + 1) spacetime. The authors consider a gravitating source that behaves as pressureless dust in the external (our) space but possesses an arbitrary equation‑of‑state parameter Ω in the internal space, i.e. p_int = Ω ρ_int. By expanding the (4 + d)‑dimensional Einstein equations to order 1/c², they obtain the perturbed metric components.

The key result is that the external g₀₀ component splits into two contributions: the standard Newtonian potential of General Relativity (GR) and an additional Yukawa‑type term, \