Relativistic dissipative hydrodynamics from kinetic theory with relaxation time approximation

TL;DR

This paper derives relativistic dissipative hydrodynamics equations directly from kinetic theory using the relaxation time approximation, resulting in improved agreement with Boltzmann simulations over traditional methods.

Contribution

It presents a new derivation of hydrodynamic equations with different coefficients, showing better alignment with numerical Boltzmann solutions and including higher-order corrections.

Findings

Derived hydrodynamic equations with different coefficients from traditional methods.

Demonstrated improved agreement with Boltzmann equation solutions.

Showed that higher-order corrections enhance the model's accuracy.

Abstract

Starting from Boltzmann equation with relaxation time approximation for the collision term and using Chapman-Enskog like expansion for 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 second moment of Boltzmann equation, the coefficients obtained are different. In the case of one-dimensional scaling expansion, we demonstrate that our results are in better agreement with numerical solution of 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.