We analyze a class of physical properties, forming the content of the so-called von Zeipel theorem, which characterizes stationary, axisymmetric, non-selfgravitating perfect fluids in circular motion in the gravitational field of a compact object. We consider the extension of the theorem to the magnetohydrodynamic regime, under the assumption of an infinitely conductive fluid, both in the Newtonian and in the relativistic framework. When the magnetic field is toroidal, the conditions required by the theorem are equivalent to integrability conditions, as it is the case for purely hydrodynamic flows. When the magnetic field is poloidal, the analysis for the relativistic regime is substantially different with respect to the Newtonian case and additional constraints, in the form of PDEs, must be imposed on the magnetic field in order to guarantee that the angular velocity Ω depends only on the specific angular momentum ℓ. In order to deduce such physical constraints, it is crucial to adopt special coordinates, which are adapted to the Ω = const surfaces. The physical significance of these results is briefly discussed.

Von Zeipel's Theorem for a Magnetized Circular Flow around a Compact Object / Zanotti, O.; Pugliese, Daniela. - In: GENERAL RELATIVITY AND GRAVITATION. - ISSN 0001-7701. - 2014, 47:44(2015). [10.1007/s10714-015-1886-4]

Von Zeipel's Theorem for a Magnetized Circular Flow around a Compact Object

Zanotti, O.;
2015-01-01

Abstract

We analyze a class of physical properties, forming the content of the so-called von Zeipel theorem, which characterizes stationary, axisymmetric, non-selfgravitating perfect fluids in circular motion in the gravitational field of a compact object. We consider the extension of the theorem to the magnetohydrodynamic regime, under the assumption of an infinitely conductive fluid, both in the Newtonian and in the relativistic framework. When the magnetic field is toroidal, the conditions required by the theorem are equivalent to integrability conditions, as it is the case for purely hydrodynamic flows. When the magnetic field is poloidal, the analysis for the relativistic regime is substantially different with respect to the Newtonian case and additional constraints, in the form of PDEs, must be imposed on the magnetic field in order to guarantee that the angular velocity Ω depends only on the specific angular momentum ℓ. In order to deduce such physical constraints, it is crucial to adopt special coordinates, which are adapted to the Ω = const surfaces. The physical significance of these results is briefly discussed.
2015
44
Zanotti, O.; Pugliese, Daniela
Von Zeipel's Theorem for a Magnetized Circular Flow around a Compact Object / Zanotti, O.; Pugliese, Daniela. - In: GENERAL RELATIVITY AND GRAVITATION. - ISSN 0001-7701. - 2014, 47:44(2015). [10.1007/s10714-015-1886-4]
File in questo prodotto:
File Dimensione Formato  
1412.6447.pdf

accesso aperto

Tipologia: Pre-print non referato (Non-refereed preprint)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 208.05 kB
Formato Adobe PDF
208.05 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/408134
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 23
social impact