Gravitational Interaction in the Chimney Lattice Universe


Eingorn M., McLaughlin A., Canay E., Brilenkov M., Zhuk A.

UNIVERSE, vol.7, no.4, 2021 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.3390/universe7040101
  • Journal Name: UNIVERSE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, Directory of Open Access Journals
  • Keywords: spatial topology, gravitational potential, Yukawa interaction, COSMOLOGICAL PERTURBATIONS, TOPOLOGY
  • Istanbul Technical University Affiliated: Yes

Abstract

We investigate the influence of the chimney topology TxTxR 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.