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

Development of a new framework for deriving order-by-order hydrodynamics from the Boltzmann equation is necessary to address the violations of conservation laws caused by the widely used Anderson-Witting formalism when relaxation-time depends on particle energy or in a hydrodynamic frame other than the Landau frame. In this study, we generalize an existing framework and extend the Anderson-Witting relaxation-time approximation to derive relativistic dissipative hydrodynamics consistently. The present framework is compatible with conservation laws and yields first-order hydrodynamic equations in the Landau frame. Additionally, corrections to the transport coefficients due to energy dependence of the relaxation-time are observed, indicating deviations from the Anderson-Witting approximation.