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Magnetohydrodynamics in stationary and axisymmetric spacetimes: a fully covariant approach
General Relativity and Quantum Cosmology · Submitted 18 Jan 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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A fully geometrical treatment of general relativistic magnetohydrodynamics (GRMHD) 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 GRMHD. 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A fully geometrical treatment of general relativistic magnetohydrodynamics (GRMHD) is developed under the hypotheses of perfect conductivity, stationarity and axisymmetry. | contribution 0.96 | 0.93 | 0.15 | asserted 1.00 |
| s1 | The spacetime is not assumed to be circular, which allows for greater generality than the Kerr-type spacetimes usually considered in GRMHD. | contribution 0.66 | 0.50 | 0.06 | asserted 0.98 |
| s2 | 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. | method 0.51 | 0.93 | 0.16 | asserted 1.00 |
| s3 | 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. | result 0.62 | 0.95 | 0.47 | asserted 1.00 |
| s4 | 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. | result 0.80 | 0.97 | 0.13 | asserted 1.00 |
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Original abstract
A fully geometrical treatment of general relativistic magnetohydrodynamics (GRMHD) 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 GRMHD. 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.
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References
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3 arXiv papers cite this in 3 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 1 paper
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This particular form is quite useful when the fluid configuration possesses certain symmetries [ref] .
Initial data for binary neutron stars with adjustable eccentricity · Euler equation · 0.86
What it cites · 2 sentences without a confident label
Cites as background 2 papers
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General relativistic magnetohydrodynamics (GRMHD) is a rapidly developing field of modern astrophysics [ref] , driven by numerous observations of accretion disks around black holes [ref] , jets in active galactic nuclei or microquasars [ref] , gamma ray bursts, hypernovae, pulsars [ref] and strongly magnetized neutrons stars (magnetars).
Magnetic acceleration of relativistic jets · Introduction · 0.99
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We assume that the spacetime $(,g)$ possesses two symmetries: (i) stationarity: there exists a group action of $(,+)$ on $$ whose orbits are timelike curves and which leaves $g$ invariant; (ii) axisymmetry: there exists a group action of $SO(2)$ on $$ whose fixed points form a 2-dimensional submanifold $Δ⊂$ and which leaves $g$ invariant (see e.g. Ref. [ref] for an extended discussion). $Δ$ is called the rotation axis.
An introduction to the theory of rotating relativistic stars · Stationary and axisymmetric spacetimes · 0.95
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