Extended relaxation time approximation and relativistic dissipative hydrodynamics

Development of a new framework for derivation order-by-order hydrodynamics from Boltzmann equation is necessary as the widely used Anderson-Witting formalism leads to violation fundamental conservation laws when relaxation-time depends on particle energy, or in hydrodynamic frame other than Landau frame. We generalize an existing consistent relativistic dissipative with energy-dependent by extending approximation. argue that present compatible and derive first-order equations landau Further, we show transport coefficients, such shear bulk viscosity well charge heat diffusion currents, have corrections due energy dependence compared what one obtains approximation collision term. The ratios these coefficients are studied using parametrized relaxation-time, several interesting scaling features reported.