Gravitational Interaction in the Chimney Lattice Universe
We investigate the influence of the chimney topology <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mo>×</mo><mi>T</mi><mo>×</mo><mi>R</...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/7/4/101 |
| _version_ | 1797537605244420096 |
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| author | Maxim Eingorn Andrew McLaughlin Ezgi Canay Maksym Brilenkov Alexander Zhuk |
| author_facet | Maxim Eingorn Andrew McLaughlin Ezgi Canay Maksym Brilenkov Alexander Zhuk |
| author_sort | Maxim Eingorn |
| collection | DOAJ |
| description | We investigate the influence of the chimney topology <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mo>×</mo><mi>T</mi><mo>×</mo><mi>R</mi></mrow></semantics></math></inline-formula> 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. |
| first_indexed | 2024-03-10T12:18:37Z |
| format | Article |
| id | doaj.art-aa0cc48a1e484472a82548000579bc88 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-10T12:18:37Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-aa0cc48a1e484472a82548000579bc882023-11-21T15:42:46ZengMDPI AGUniverse2218-19972021-04-017410110.3390/universe7040101Gravitational Interaction in the Chimney Lattice UniverseMaxim Eingorn0Andrew McLaughlin1Ezgi Canay2Maksym Brilenkov3Alexander Zhuk4Department of Mathematics and Physics, North Carolina Central University, 1801 Fayetteville St., Durham, NC 27707, USADepartment of Mathematics and Physics, North Carolina Central University, 1801 Fayetteville St., Durham, NC 27707, USADepartment of Physics, Istanbul Technical University, Maslak, 34469 Istanbul, TurkeyInstitute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, N-0315 Oslo, NorwayAstronomical Observatory, Odessa I.I. Mechnikov National University, Dvoryanskaya St. 2, 65082 Odessa, UkraineWe investigate the influence of the chimney topology <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mo>×</mo><mi>T</mi><mo>×</mo><mi>R</mi></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2218-1997/7/4/101spatial topologygravitational potentialYukawa interaction |
| spellingShingle | Maxim Eingorn Andrew McLaughlin Ezgi Canay Maksym Brilenkov Alexander Zhuk Gravitational Interaction in the Chimney Lattice Universe Universe spatial topology gravitational potential Yukawa interaction |
| title | Gravitational Interaction in the Chimney Lattice Universe |
| title_full | Gravitational Interaction in the Chimney Lattice Universe |
| title_fullStr | Gravitational Interaction in the Chimney Lattice Universe |
| title_full_unstemmed | Gravitational Interaction in the Chimney Lattice Universe |
| title_short | Gravitational Interaction in the Chimney Lattice Universe |
| title_sort | gravitational interaction in the chimney lattice universe |
| topic | spatial topology gravitational potential Yukawa interaction |
| url | https://www.mdpi.com/2218-1997/7/4/101 |
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