Weak-field limit of Kaluza-Klein models with spherical compactification: problematic aspects

TL;DR

This paper examines the weak-field limit of Kaluza-Klein models with spherical internal space, revealing that the predicted post-Newtonian parameter significantly deviates from observed values, raising issues with the model's viability.

Contribution

It provides a detailed analysis of gravitational tests in Kaluza-Klein models with spherical compactification, highlighting problematic predictions for the parameterized post-Newtonian parameter.

Findings

The PPN parameter γ equals 1/3 in this model.

The model's predictions contradict observational data.

The analysis exposes issues with the model's physical viability.

Abstract

We investigate classical gravitational tests for the Kaluza-Klein model with spherical compactification of the internal two-dimensional space. In the case of the absence of a multidimensional bare cosmological constant, the only matter which corresponds to the proposed metric ansatz is a perfect fluid with the vacuum equation of state in the external space and the dust-like equation of state in the internal space. We perturb this background by a compact massive source with the dust-like equation of state in both external and internal spaces (e.g., a point-like mass), and obtain the metric coefficients in the weak-field approximation. It enables to calculate the parameterized post-Newtonian parameter $\gamma$. We demonstrate that $\gamma=1/3$ which strongly contradicts the observations.