相对论磁流体力学中的物态方程：变绝热指数与常绝热指数
Equation of State in Relativistic Magnetohydrodynamics: variable versus constant adiabatic index
摘要：
状态方程的作用，一个完美的传导，相对论磁化流体是这项工作的主要课题。理想的常数$Γ$定律状态方程，通常采用在广泛的天体物理应用，比较与更现实的状态方程，更好地近似的单物种相对论气体。本文围绕三个不同的主题展开。首先，一个更现实的状态方程的快速磁声冲击的传播的影响进行了研究。这就质疑了恒定的$Γ$定律状态方程在气体温度在磁流体波中发生实质性变化的问题中的有效性。其次，我们提出了一个新的反演方案，以恢复原始变量（如静止质量密度和压力）从保守的，允许一个通用的状态方程，并避免灾难性的数值取消在非相对论和超相对论的限制。最后，选定的数值试验的天体物理学的相关性（包括磁化吸积流克尔黑洞周围）进行了比较，使用不同的状态方程。我们的主要结论是，一个现实的状态方程的选择可以大大承担的解决方案时，从冷到热气体（反之亦然）的过渡。在这种情况下，多方状态方程会严重危及解。
英文摘要：
The role of the equation of state for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant $Γ$-law equation of state, commonly adopted in a wide range of astrophysical applications, is compared with a more realistic equation of state that better approximates the single-specie relativistic gas. The paper focus on three different topics. First, the influence of a more realistic equation of state on the propagation of fast magneto-sonic shocks is investigated. This calls into question the validity of the constant $Γ$-law equation of state in problems where the temperature of the gas substantially changes across hydromagnetic waves. Second, we present a new inversion scheme to recover primitive variables (such as rest-mass density and pressure) from conservative ones that allows for a general equation of state and avoids catastrophic numerical cancellations in the non-relativistic and ultrarelativistic limits. Finally, selected numerical tests of astrophysical relevance (including magnetized accretion flows around Kerr black holes) are compared using different equations of state. Our main conclusion is that the choice of a realistic equation of state can considerably bear upon the solution when transitions from cold to hot gas (or viceversa) are present. Under these circumstances, a polytropic equation of state can significantly endanger the solution.
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