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Causality and stability analysis of first-order field redefinition in relativistic hydrodynamics from kinetic theory

In this work, the causality and stability of a first-order relativistic dissipative hydrodynamic theory, that redefines the hydrodynamic fields from a first principle microscopic estimation, have been analyzed. A generic approach of gradient expansion for solving the relativistic transport equation has been adopted using the Chapman-Enskog iterative method. Next, the momentum dependent relaxation time approximation (MDRTA) has been employed to quantify the collision term for analytical estimation of the field correction coefficients from kinetic theory. At linear regime, in local rest frame the dispersion relations are observed to produce a causal propagating mode. However, the acausality and instability reappear when a boosted background is considered for linear analysis. These facts point out relevant aspects regarding the methodology of extracting the causal and stable first order hydrodynamics from kinetic theory and indicate the appropriate approach to construct a valid first order theory with proper justification.