Interior potential of a toroidal shell from pole values

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985815%3A_____%2F19%3A00518042" target="_blank" >RIV/67985815:_____/19:00518042 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1093/mnras/stz1226" target="_blank" >https://doi.org/10.1093/mnras/stz1226</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/mnras/stz1226" target="_blank" >10.1093/mnras/stz1226</a>

Result language
angličtina
Original language name
Interior potential of a toroidal shell from pole values
Original language description
We have investigated the toroidal analogue of ellipsoidal shells of matter, which are of great significance in Astrophysics. The exact formula for the gravitational potential klf (R, Z)of a shell with a circular section at the pole of toroidal coordinates is first established. It depends on the mass of the shell, its main radius and axial ratio e (i.e. core-to-main radius ratio), and involves the product of the complete elliptic integrals of the first and second kinds.Numerical experiments confirm the great reliability of the approach, in particular for small-to-moderate axial ratios (e2 < 0.1 typically). In contrast with the ellipsoidal case (Newton's theorem), the potential is 1101 uniform inside the shell cavity as a consequence of the curvature. We explain how to construct the interior potential of toroidal shells with a thick edge (i.e. tubes), and how a core stratification can be accounted for. This is a new step towards the full description of the gravitating potential and forces of tori and rings. Applications also concern electrically charged systems, and thus go beyond the context of gravitation.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10308 - Astronomy (including astrophysics,space science)

Project
<a href="/en/project/GC19-01137J" target="_blank" >GC19-01137J: Largest black holes in the sky: origin and evolution of horizon-scale structures</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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