标题： 绕致密天体磁化圆流的Von Zeipel定理 显示英文标题

标题： Von Zeipel's theorem for a magnetized circular flow around a compact object

摘要： 我们分析了一类物理性质，构成了所谓的von Zeipel定理的内容，该定理描述了在致密天体引力场中作圆周运动的静态、轴对称、非自引力的理想流体的特性。 我们考虑在无限导电流体假设下，该定理向磁流体动力学区域的扩展，包括牛顿和相对论框架。 当磁场为环形时，定理所需的条件等价于可积性条件，这与纯流体动力学流动的情况类似。 当磁场为极向时，相对论区域的分析与牛顿时的情况有显著不同，必须对磁场施加额外的约束，以保证角速度$\Omega$仅依赖于比角动量$\ell$。 为了推导这些物理约束，采用适应于$\Omega={\rm const}$表面的特殊坐标是至关重要的。 这些结果的物理意义进行了简要讨论。 显示英文摘要

摘要： 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 $\Omega$ depends only on the specific angular momentum $\ell$. In order to deduce such physical constraints, it is crucial to adopt special coordinates, which are adapted to the $\Omega={\rm const}$ surfaces. The physical significance of these results is briefly discussed.