相对论粘性无阻磁流体动力学中的因果性和稳定性
Causality and stability in relativistic viscous non-resistive magneto-fluid dynamics
摘要：
我们调查的因果关系和稳定性的相对论性粘性磁流体力学的Israel-Stewart（IS）的二阶理论的框架内，也在一个修改后的IS理论，其中包括磁场的影响，在松弛方程的粘性应力。我们通过在流体变量的平衡值附近扰动流体变量来计算色散关系。在理想磁流体力学极限下，线性色散关系产生了著名的传播模式：Alfvén模式和磁声模式，在体粘压力存在下，因果关系界与磁场的大小无关.当我们用特征线法取方程的完全非线性形式时，同样的界限也是正确的。在剪切粘性压力的存在下，因果关系的界限是独立的磁场的大小为两个磁声模式。然而，剪切-阿尔芬模式的因果关系界取决于传播的大小和方向。对于修正的IS理论，在剪切粘性的存在下，新的非流体动力学模式出现，但渐近因果关系的条件是相同的IS。总之，虽然磁场确实影响流体中的波传播，但在流体静止框架中对稳定性和渐近因果性条件的研究表明，如果它们服从一定的渐近因果性条件，则流体保持稳定和因果性。
英文摘要：
We investigate the causality and the stability of the relativistic viscous magneto-hydrodynamics in the framework of the Israel-Stewart (IS) second-order theory, and also within a modified IS theory which incorporates the effect of magnetic fields in the relaxation equations of the viscous stress. We compute the dispersion relation by perturbing the fluid variables around their equilibrium values. In the ideal magnetohydrodynamics limit, the linear dispersion relation yields the well-known propagating modes: the Alfvén and the magneto-sonic modes.In the presence of bulk viscous pressure, the causality bound is found to be independent of the magnitude of the magnetic field. The same bound also remains true, when we take the full non-linear form of the equation using the method of characteristics. In the presence of shear viscous pressure, the causality bound is independent of the magnitude of the magnetic field for the two magneto-sonic modes. The causality bound for the shear-Alfvén modes, however, depends both on the magnitude and the direction of the propagation. For modified IS theory in the presence of shear viscosity, new non-hydrodynamic modes emerge but the asymptotic causality condition is the same as that of IS. In summary, although the magnetic field does influence the wave propagation in the fluid, the study of the stability and asymptotic causality conditions in the fluid rest frame shows that the fluid remains stable and causal given that they obey certain asymptotic causality condition.
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