https://doi.org/10.1140/epjc/s10052-013-2700-7
Regular Article - Theoretical Physics
Many-body problem in Kaluza–Klein models with toroidal compactification
1
Department of Theoretical Physics, Odessa National University, Dvoryanskaya st. 2, Odessa, 65082, Ukraine
2
Astronomical Observatory, Odessa National University, Dvoryanskaya st. 2, Odessa, 65082, Ukraine
3
Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Shevchenko av. 1, Odessa, 65044, Ukraine
4
CREST and NASA Research Centers, North Carolina Central University, Fayetteville st. 1801, Durham, NC, 27707, USA
* e-mail: maxim.eingorn@gmail.com
Received:
24
June
2013
Accepted:
11
December
2013
Published online:
23
January
2014
In this paper, we consider a system of gravitating bodies in Kaluza–Klein models with toroidal compactification of the extra dimensions. To simulate the astrophysical objects (e.g., our Sun and pulsars) with energy density much greater than the pressure, we assume that these bodies are pressureless in the external space, i.e., the space we inhabit. At the same time, they may have nonzero parameters 
in the equations of state in the extra dimensions. We construct the Lagrange function of this many-body system for any value of 
. Moreover, the gravitational tests (PPN parameters, perihelion and periastron advances) require a negligible deviation from the latent soliton value 
. 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 KK modes. This looks very unnatural from the point of view of quantum physics.
© The Author(s), 2014
