Magnetohydrodynamics in stationary and axisymmetric spacetimes : a fully covariant approach
Magnetohydrodynamics in stationary and axisymmetric spacetimes : a fully covariant approach
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静止和轴对称时空中的磁流体动力学：一种完全协变的方法
DOI：
10.1103/physrevd.83.104007
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
and Yoshiharu Eriguchi
中科院分区：
文献类型：
--
作者：
Eric Gourgoulhon;Charalampos Markakis;Koji Uryu;and Yoshiharu Eriguchi
在完全导电性、平稳性和轴对称的假设下，对广义相对论磁流体力学进行了完全的几何处理。时空不是假定为圆形的，这比广义相对论磁流体动力学中通常考虑的克尔型时空具有更大的普遍性。将电磁场张量单独表示为与时空对称性相关的三个标量场，在各个方向上推广了先前得到的结果。特别地，我们给出了Soloviev跨场方程的第一个相对论版本，它的子情况导致了流体动力极限下的Grad-Shafranov方程和Stokes方程的完全协变版本。作为相对论索洛维耶夫方程的另一个子例，我们还推导出了在静止和轴对称时空中具有纯环面磁场的磁流体动力学平衡方程。
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.