Polytropic representation of non-isotropic kinetic pressure tensor for non-ideal plasma fluids in relativistic jets

Non-ideal fluids are likely to be affected by the occurrence of pressure anisotropy effects, whose understanding for relativistic systems requires knowledge of the energy-momentum tensor. In this paper, the case of magnetized jet plasmas at equilibrium is considered, in which both microscopic velocities of constituent particles and the continuum fluid flow are treated as relativistic ones. A theoretical framework based on covariant statistical kinetic approach is implemented, which permits the proper treatment of single-particle and phase-space kinetic constraints and, ultimately, the calculation of the system continuum fluid fields associated with physical observables. A Gaussian-like solution for the kinetic distribution function (KDF) is constructed, in which the physical mechanism responsible for the generation of temperature anisotropy is identified with magnetic moment conservation. A Chapman-Enskog representation of the same KDF is then obtained in terms of expansion around an equilibrium isotropic Juttner distribution. This permits the analytical calculation of the fluid 4-flow and stress-energy tensor and the consequent proof that the corresponding kinetic pressure tensor is non-isotropic. As a notable result, the validity of a polytropic representation for the perturbative non-isotropic pressure contributions is established, whereby directional pressures exhibit specific power-law functional dependences on fluid density.