Hamiltonian theory of relativistic magnetohydrodynamics with anisotropic pressure

Abstract
This Brief Communication introduces a special relativistic extension of ideal magnetohydrodynamics having anisotropic pressure, and provides its Hamiltonian formulation in a fixed inertial frame. The nonrelativistic limit of this theory recovers the ‘‘double adiabatic’’ hydromagnetic equations of Chew, Goldberger, and Low [Proc. R. Soc. London Ser. A 2 3 6, 112 (1956)]. For isotropic pressure distribution the equations and Hamiltonian structure reduce to the usual theory of relativistic magnetohydrodynamics. The Poisson bracket for the system is not symplectic. Rather, it is dual to a Lie algebra of semidirect‐product type.