Relativistic magnetohydrodynamics. (English) Zbl 1380.83108
Summary: We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the “conventional” magnetohydrodynamics (formulated using Maxwell’s equations in matter) to those in the “dual” version of magnetohydrodynamics (formulated using the conserved magnetic flux).
MSC:
| 83C55 | Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) |
| 76Y05 | Quantum hydrodynamics and relativistic hydrodynamics |
| 81V05 | Strong interaction, including quantum chromodynamics |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 80A10 | Classical and relativistic thermodynamics |
| 83C22 | Einstein-Maxwell equations |
| 78A25 | Electromagnetic theory (general) |
| 83-02 | Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory |
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