Gravitational Interaction in the Chimney Lattice Universe †
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Дата
2021
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Анотація
We investigate the influence of the chimney topology T T R of the Universe on the
gravitational potential and force that are generated by point-like massive bodies. We obtain three
distinct expressions for the solutions. One follows from Fourier expansion of delta functions into
series using periodicity in two toroidal dimensions. The second one is the summation of solutions of
the Helmholtz equation, for a source mass and its infinitely many images, which are in the form of
Yukawa potentials. The third alternative solution for the potential is formulated via the Ewald sums
method applied to Yukawa-type potentials. We show that, for the present Universe, the formulas
involving plain summation of Yukawa potentials are preferable for computational purposes, as they
require a smaller number of terms in the series to reach adequate precision.
Опис
Ключові слова
spatial topology, gravitational potential, Yukawa interaction
Бібліографічний опис
Universe