Classical tests of multidimensional gravity: negative result

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.