Gravitational potentials and forces in the Lattice Universe: a slab
Department of Mathematics and Physics, North Carolina Central University, 1801 Fayetteville St., 27707, Durham, NC, USA
2 Institute of Theoretical Astrophysics, University of Oslo, Postboks 1029 Blindern, 0315, Oslo, Norway
3 Astronomical Observatory, Odessa I.I. Mechnikov National University, Dvoryanskaya St. 2, 65082, Odessa, Ukraine
Accepted: 20 January 2021
Published online: 12 February 2021
We study the effect of the slab topology of the Universe on the form of gravitational potentials and forces created by point-like masses. We obtain two alternative forms of solutions: One is based on the Fourier series expansion of the delta function using the periodical property along the toroidal dimension, and another one is derived by direct summation of solutions of the Helmholtz equation for the source particle and all its images. The latter one takes the form of the sum of Yukawa-type potentials. We demonstrate that for the present Universe the latter solution is preferable for numerical calculations since it requires less terms of the series to achieve the necessary precision.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021