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

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 Ω) in the internal space. In the single-component case, tension (Ω = −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 Ω = −1/2, but the second one is of special interest because it is free of tension, i.e. Ω = 0. To obtain this result, we need to impose certain conditions.

Weak-Field Limit of a Kaluza-Klein Model with a Nonlinear Perfect Fluid

“…In paper [10], an interesting example of a model with spherical compactification was demonstrated; the bare gravitating mass without tension was shown to achieve agreement with observations while effective relativistic pressure in the external/our space was successfully avoided. The result was obtained through fine tuning between the components of a multicomponent background perfect fluid with linear equations of state.…”

“…However, fluctuations of background matter concentrate around the gravitating mass and the bare gravitating mass gets covered by this coat to attain effective relativistic pressure in the external space. Certainly, this contradicts the observations (e.g., Sun does not have such relativistic pressure) and the only way to avoid such problem is to introduce, again, tension in the internal space [10,14].…”

“…Obviously, such multidimensional theories should not contradict the experimental data, in particular, the well-known gravitational tests in the Solar system: deflection of light, time delay of radar echoes and perihelion precession of Mercury. We investigated this problem in a number of our previous papers [5][6][7][8][9][10][11][12] and one of the main conclusions of these papers is that in the case of Ricci-flat internal spaces, the model with pressureless gravitating mass contradicts gravitational tests [5]. The negative result follows as a consequence of massless fluctuations of the internal space that generate the fifth force [13].…”

Discrete symmetries in the Kaluza-Klein theories

“…These studies are for the two cases, presented in this paper, under consideration. There are, however, several proposals in the literature which suggest the compactification scheme and discuss it [54,55]. We are not yet able to comment them from the point of view of our two discussed cases.…”

“…There are several papers in the literature [31,32,54,55] studying the way of compactification. It is not easy to say whether the experiences from this literature can usefully be used in our cases.…”