Kaluza-Klein models with spherical compactification: observational constraints and possible examples

TL;DR

This paper explores Kaluza-Klein models with spherical internal spaces, identifying conditions under which these models align with gravitational and thermodynamical observations, including models with tension and tension-free internal matter.

Contribution

It introduces new multicomponent Kaluza-Klein models that satisfy observational constraints, including a tension-free model with internal matter.

Findings

Single-component models require tension for observational consistency.

Two multicomponent models satisfy both gravitational and thermodynamical tests.

A tension-free model with zero internal matter equation of state is proposed.

Abstract

We consider Kaluza-Klein models with background matter in the form of a multicomponent perfect fluid. This matter provides 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. In the single-component case, tension ($\Omega=-1/2$) is the necessary condition to satisfy both the gravitational tests in the solar system and the thermodynamical observations. In the multicomponent case, we propose two models satisfying both of these observations. One of them also requires tension $\Omega=-1/2$, but the second one is of special interest because is free of tension, i.e. $\Omega=0$. To get this result, we need to impose certain conditions.