Relativistic dissipative hydrodynamics from kinetic theory with relaxation-time approximation

Starting from the Boltzmann equation with the relaxation time approximation for the collision term and using a Chapman-Enskog-like expansion for the distribution function close to equilibrium, we derive hydrodynamic evolution equations for the dissipative quantities directly from their definition. Although the form of the equations is identical to those obtained in traditional Israel-Stewart approaches employing Grad's 14-moment approximation and the second moment of the Boltzmann equation, the coefficients obtained are different. In the case of a one-dimensional scaling expansion, we demonstrate that our results are in better agreement with a numerical solution of the Boltzmann equation as compared to Israel-Stewart results. We also show that including approximate higher-order corrections in viscous evolution significantly improves this agreement, thus justifying the relaxation time approximation for the collision term.