Magnetohydrodynamics in stationary and axisymmetric spacetimes: A fully covariant approach

Journal Article · Sun May 15 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.104007· OSTI ID:21502578

Gourgoulhon, Eric ^[1]; Markakis, Charalampos ^[2]; Uryu, Koji ^[3]; Eriguchi, Yoshiharu ^[4]

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

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.

• OSTI ID: 21502578
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 10; Other Information: DOI: 10.1103/PhysRevD.83.104007; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AXIAL SYMMETRY
ELECTROMAGNETIC FIELDS
EQUILIBRIUM
GRAD-SHAFRANOV EQUATION
HYPOTHESIS
KERR FIELD
MAGNETIC FIELDS
MAGNETOHYDRODYNAMICS
RELATIVISTIC RANGE
SCALAR FIELDS
SPACE-TIME
DIFFERENTIAL EQUATIONS
ENERGY RANGE
EQUATIONS
FLUID MECHANICS
GRAVITATIONAL FIELDS
HYDRODYNAMICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY