Magnetohydrodynamics in stationary and axisymmetric spacetimes: A fully covariant approach

Eric Gourgoulhon, Charalampos Markakis, Kōji Uryū, and Yoshiharu Eriguchi
Phys. Rev. D 83, 104007 – Published 3 May 2011

Abstract

A fully geometrical treatment of general relativistic magnetohydrodynamics is developed under the hypotheses of perfect conductivity, stationarity, and axisymmetry. The spacetime is not assumed to be circular, which allows for greater generality than the Kerr-type spacetimes usually considered in general relativistic magnetohydrodynamics. Expressing the electromagnetic field tensor solely in terms of three scalar fields related to the spacetime symmetries, we generalize previously obtained results in various directions. In particular, we present the first relativistic version of the Soloviev transfield equation, subcases of which lead to fully covariant versions of the Grad-Shafranov equation and of the Stokes equation in the hydrodynamical limit. We have also derived, as another subcase of the relativistic Soloviev equation, the equation governing magnetohydrodynamical equilibria with purely toroidal magnetic fields in stationary and axisymmetric spacetimes.

  • Received 18 January 2011

DOI:https://doi.org/10.1103/PhysRevD.83.104007

© 2011 American Physical Society

Authors & Affiliations

Eric Gourgoulhon1,*, Charalampos Markakis2,†, Kōji Uryū3,‡, and Yoshiharu Eriguchi4,§

  • 1Laboratoire Univers et Théories, UMR 8102 du CNRS, Observatoire de Paris, Université Paris Diderot, F-92190 Meudon, France
  • 2Department of Physics, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201, USA
  • 3Department of Physics, University of the Ryukyus, Senbaru, Nishihara, Okinawa 903-0213, Japan
  • 4Department of Earth Science and Astronomy, Graduate School of Arts and Sciences, University of Tokyo, Komaba, Meguro-ku, 3-8-1, 153-8902 Tokyo, Japan

  • *eric.gourgoulhon@obspm.fr
  • markakis@uwm.edu
  • uryu@sci.u-ryukyu.ac.jp
  • §eriguchi@esa.c.u-tokyo.ac.jp

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 83, Iss. 10 — 15 May 2011

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×