Extended relaxation time approximation and relativistic dissipative hydrodynamics

Development of a new framework for derivation of order-by-order hydrodynamics from Boltzmann equation is necessary as the widely used Anderson-Witting formalism leads to violation of fundamental conservation laws when the relaxation-time depends on particle energy, or in a hydrodynamic frame other than the Landau frame. We generalize an existing framework for consistent derivation of relativistic dissipative hydrodynamics from the Boltzmann equation with an energy-dependent relaxation-time by extending the Anderson-Witting relaxation-time approximation. We argue that the present framework is compatible with conservation laws and derive first-order hydrodynamic equations in landau frame. Further, we show that the transport coefficients, such as shear and bulk viscosity as well as charge and heat diffusion currents, have corrections due to the energy dependence of relaxation-time compared to what one obtains from the Anderson-Witting approximation of the collision term. The ratios of these transport coefficients are studied using a parametrized relaxation-time, and several interesting scaling features are reported. (C) 2022 The Author(s). Published by Elsevier B.V.

Automated summary

In this study, a new framework for deriving relativistic dissipative hydrodynamics from the Boltzmann equation with energy-dependent relaxation time is developed. The framework is shown to be compatible with conservation laws and corrections to transport coefficients due to energy dependence of relaxation time are discussed. The ratios of these transport coefficients are studied using a parametrized relaxation-time, revealing interesting scaling features.