Alexey Chopovsky, Maxim Eingorn, Alexander Zhuk
In this paper, 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 show that the presence of pressure/tension in the extra dimensions leads necessarily to the uniform smearing of the gravitating bodies over the internal space. Then, 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/1302.0501
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