Many-body problem in Kaluza-Klein models with toroidal compactification

Abstract

In this paper, we consider a system of gravitating bodies in Kaluza-Klein models with toroidal compactification of extra dimensions. To simulate the astrophysical objects (e.g., our Sun and pulsars) with energy density much greater than pressure, we suppose that these bodies are pressureless in the external/our space. At the same time, they may have nonzero parameters \omega_{(\bar\alpha -3)} \, (\bar\alpha =4,\ldots,D) of the equations of state in the extra dimensions. We construct the Lagrange function of this many-body system for any value of \Sigma =\sum_{\bar\alpha} \omega_{(\bar\alpha -3)}. Moreover, the gravitational tests (PPN parameters, perihelion and periastron advances) require negligible deviation from the latent soliton value \Sigma =-(D-3)/2. However, the presence of pressure/tension in the internal space results necessarily in the smearing of the gravitating masses over the internal space and in the absence of the KK modes. This looks very unnatural from the point of view of quantum physics.