| In this work the linear fluid transport equations for relativistic and collisionless plasmas are exactly derived. At this end, the relativistic Vlasov equation perturbed with respect to the global equilibrium has been analytically solved. The mathematical method for solving the Vlasov equation is based on the expansion of the distribution function on the Legendre polynomial basis and on the use of the continued fractions to incorporate the contributions from all the Legendre modes. The transport coefficients corresponding to the generalized heat flux and stress tensor have been deduced. These coefficients constitute exact closure relations for the fluid transport quations to describe small perturbation in relativistic and collisionless plasmas. In addition the fluid response function was calculated and it is shown that it corresponds exactly to the kinetic one |
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