Classical tests of multidimensional gravity: negative result

TL;DR

This paper investigates classical gravitational tests within multidimensional Kaluza-Klein models, finding that only three-dimensional space aligns with experimental data, implying extra dimensions do not influence observable gravitational phenomena.

Contribution

The study derives metric coefficients and gravitational test formulas in a multidimensional setting, revealing that extra dimensions do not affect classical tests, thus challenging the viability of such models.

Findings

Formulas match general relativity in frequency shift

Perihelion shift and light deflection formulas depend on total dimensions D

Only for D=3 do predictions agree with experiments

Abstract

In Kaluza-Klein model with toroidal extra dimensions, we obtain the metric coefficients in a weak-field approximation for delta-shaped matter sources. These metric coefficients are applied to calculate the formulas for frequency shift, perihelion shift, deflection of light and parameterized post-Newtonian (PPN) parameters. In the leading order of approximation, the formula for frequency shift coincides with well-known general relativity expression. However, for perihelion shift, light deflection and PPN parameter $\gamma $ we obtain formulas $D\pi r_g/[(D-2)a(1-e^2)]$, $(D-1)r_g/[(D-2)\rho]$ and $1/(D-2)$ respectively, where $D$ is a total number of spatial dimensions. These expressions demonstrate good agreement with experimental data only in the case of ordinary three-dimensional $(D=3)$ space. This result does not depend on the size of the extra dimensions. Therefore, in the considered multidimensional Kaluza-Klein models the point-like masses cannot produce the gravitational field which corresponds to the classical gravitational tests.