Interior potential of a toroidal shell from pole values

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Interior potential of a toroidal shell from pole values

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Interior potential of a toroidal shell from pole values

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10308 - Astronomy (including astrophysics,space science)

Projekt

<a href="/cs/project/GC19-01137J" target="_blank" >GC19-01137J: Největší černé díry na obloze: vznik a vývoj struktur na škálách horizontu</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Monthly Notices of the Royal Astronomical Society

ISSN

1365-2966

e-ISSN

—

Svazek periodika

486

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

14

Strana od-do

5656-5669

Kód UT WoS článku

000474908200092

EID výsledku v databázi Scopus

2-s2.0-85067923177