无力电动力学的协变双曲化
Covariant Hyperbolization of Force-free Electrodynamics
摘要：
无力等离子体动力学（FFE）是一个非线性方程组，模拟了在磁主导的相对论等离子体存在下电磁场的演化。这种配置出现在几个天体物理场景中，这些场景代表了令人兴奋的实验室，以了解极端状态下的物理学。我们证明了这个系统，当限制到正确的约束子流形，是对称双曲。在数值应用中，将系统保持在该子流形中是不可行的，因此，有必要首先在该子流形的切空间中分析其结构，然后在其整个邻域中分析其结构。直接（或天真的）制定这一制度（在整个切空间）的结果在一个弱双曲型系统的发展方程，其中well-possednes的初始值制定不遵循。利用Geroch的广义对称双曲形式，我们引入了FFE系统的协变双曲化。事实上，与通常的Maxwell情形类似，对于约束子流形上的受限系统以及在其整个邻域中定义的适当扩展系统，我们发现了一个完整的双曲子族，然后用该族中的一个特殊的对称化子在背景时空的一般（$3+1$）分解中写出相关的演化方程。有趣的是，事实证明，对于一个特定的选择的失效和转移功能的叶理，我们的对称化系统减少到一个发现的Pfeiffer。最后，我们分析了所产生的演化系统的特征结构。
英文摘要：
Force-Free Flectrodynamics (FFE) is a non-linear system of equations modeling the evolution of the electromagnetic field, in the presence of a magnetically dominated relativistic plasma. This configuration arises on several astrophysical scenarios, which represent exciting laboratories to understand physics in extreme regimes. We show that this system, when restricted to the correct constraint submanifold, is symmetric hyperbolic. In numerical applications is not feasible to keep the system in that submanifold, and so, it is necessary to analyze its structure first in the tangent space of that submanifold and then in a whole neighborhood of it. As already shown by Pfeiffer, a direct (or naive) formulation of this system (in the whole tangent space) results in a weakly hyperbolic system of evolution equations for which well-possednes for the initial value formulation does not follows. Using the generalized symmetric hyperbolic formalism due to Geroch, we introduce here a covariant hyperbolization for the FFE system. In fact, in analogy to the usual Maxwell case, a complete family of hyperbolizers is found, both for the restricted system on the constraint submanifold as well as for a suitably extended system defined in a whole neighborhood of it. A particular symmetrizer among the family is then used to write down the pertaining evolution equations, in a generic ($3+1$)-decomposition on a background spacetime. Interestingly, it turns out that for a particular choice of the lapse and shift functions of the foliation, our symmetrized system reduces to the one found by Pfeiffer. Finally we analyze the characteristic structure of the resulting evolution system.
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