1. Gravitational potentials and forces in the Lattice Universe: a slab
- Author
-
Niah O’Briant, Alexander Zhuk, Maxim Brilenkov, Katie Arzu, and Maxim Eingorn
- Subjects
Fluid Flow and Transfer Processes ,Physics ,Cosmology and Nongalactic Astrophysics (astro-ph.CO) ,Series (mathematics) ,Helmholtz equation ,010308 nuclear & particles physics ,media_common.quotation_subject ,Lattice (group) ,FOS: Physical sciences ,General Physics and Astronomy ,Dirac delta function ,General Relativity and Quantum Cosmology (gr-qc) ,01 natural sciences ,General Relativity and Quantum Cosmology ,Universe ,Gravitation ,symbols.namesake ,Classical mechanics ,0103 physical sciences ,Slab ,symbols ,010303 astronomy & astrophysics ,Fourier series ,Astrophysics - Cosmology and Nongalactic Astrophysics ,media_common - Abstract
We study the effect of the slab topology $T\times R\times R$ 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., This is a preprint of an article published in the European Physical Journal Plus. The final authenticated version is available online at: https://doi.org/10.1140/epjp/s13360-021-01139-y
- Published
- 2021