Alexey Chopovsky, Maxim Eingorn, Alexander Zhuk
We consider a system of gravitating bodies in Kaluza-Klein models with toroidal compactification of extra dimensions. To simulate the ordinary astrophysical objects (e.g., our Sun), we suppose that these bodies have nonrelativistic (pressureless) equations of state in the external/our space. At the same time, they may have nonzero parameters \omega_{(\bar{\alpha} -3)} (\bar{\alpha} =4,...,D) of the equations of state in the extra dimensions. We prove that the Lagrange function of this many-body system can be constructed only if \Sigma =\sum_{\bar{\alpha}} \omega_{(\bar{\alpha} -3)} =0. This strongly contradicts the observations which demand \Sigma \approx (3-D)/2 \sim O(1) for D>3. Therefore, considered multidimensional Kaluza-Klein models face a severe problem.
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http://arxiv.org/abs/1301.5218
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