https://doi.org/10.1140/epjc/s10052-015-3445-2
Regular Article - Theoretical Physics
Lattice Universe: examples and problems
1
Department of Theoretical Physics, Odessa National University, Dvoryanskaya st. 2, Odessa, 65082, Ukraine
2
Physics Department, North Carolina Central University, Fayetteville st. 1801, Durham, NC, 27707, USA
3
Astronomical Observatory, Odessa National University, Dvoryanskaya st. 2, Odessa, 65082, Ukraine
* e-mail: maxim.eingorn@gmail.com
Received:
11
April
2015
Accepted:
8
May
2015
Published online:
19
May
2015
We consider lattice Universes with spatial topologies 
, 
, and 
. In the Newtonian limit of General Relativity, we solve the Poisson equation for the gravitational potential in the enumerated models. In the case of point-like massive sources in the model, we demonstrate that the gravitational potential has no definite values on the straight lines joining identical masses in neighboring cells, i.e. at points where masses are absent. Clearly, this is a nonphysical result, since the dynamics of cosmic bodies is not determined in such a case. The only way to avoid this problem and get a regular solution at any point of the cell is the smearing of these masses over some region. Therefore, the smearing of gravitating bodies in 
-body simulations is not only a technical method but also a physically substantiated procedure. In the cases of and topologies, there is no way to get any physically reasonable and nontrivial solution. The only solutions we can get here are the ones which reduce these topologies to the one.
© SIF and Springer-Verlag Berlin Heidelberg, 2015
