RG/E Derivation of Relativistic First-Order Fluid Dynamics

Abstract

AbstractWe derive the relativistic fluid dynamic equation as describing the asymptotic slow dynamics of the relativistic Boltzmann equation with quantum statistics by applying the RG/E method, as a natural extension of the analysis done for the non-relativistic case done in Chap. 8: The resultant equation is the relativistic first-order fluid dynamic equation, i.e., a relativistic analogue of the Navier-Stokes equation in the non-relativistic case. The derivation is based on a faithful solution of the Boltzmann equation based on the perturbation theory and is free from any ad hoc assumptions. The resultant equation is found to uniquely coincides with that in the energy frame. A proof is also given that our equation possesses the linear stability, irrespective of the properties of the collision term, in the sense that the equilibrium solution is stable to any linear disturbances.