Relativistic Magnetohydrodynamics from Myers-Pospelov Lorentz-Violating Electrodynamics

Abstract: We derive the equations of relativistic magnetohydrodynamics from Lorentz-violating Myers-Pospelov electrodynamics. Starting from the modified fermionic and electromagnetic equations of motion, we employ the covariant Wigner formalism to establish the semiclassical spectral constraints and distribution function, which, combined with Noether's theorem, yield the energy-momentum tensor, particle current, and corresponding conservation laws in the presence of Lorentz violation. The resulting hydrodynamic description contains Lorentz-violating corrections to the thermodynamic quantities and to the fluid currents. In the purely timelike sector, these corrections can be absorbed into effective thermodynamic quantities, preserving the isotropic structure of the fluid equations. In contrast, spacelike backgrounds introduce explicit contributions along the preferred direction, which cannot be absorbed into the standard hydrodynamic variables and give rise to anisotropic forces and torques. These effects lead to departures from standard relativistic magnetohydrodynamics and provide a direct macroscopic manifestation of the Lorentz-violating background. Our results provide a first-principles derivation of Lorentz-violating relativistic magnetohydrodynamics and establish a framework for investigating the macroscopic consequences of Lorentz violation in magnetized relativistic fluids.