Classical tests of multidimensional gravity: negative result

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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 γ we obtain formulas Dπrg/[(D-2)a(1-e²)], (D-1)rg/[(D-2)ρ] 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.