Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory

TL;DR

This paper presents a new derivation of dissipative relativistic fluid dynamics equations directly from kinetic theory, resulting in improved agreement with Boltzmann equation solutions for one-dimensional expansions.

Contribution

It introduces a novel derivation method that uses the definition of dissipative currents directly, differing from the traditional Israel-Stewart approach.

Findings

Derived equations are formally identical to previous ones but with different coefficients.

The new method aligns better with Boltzmann equation solutions in one-dimensional scaling.

Provides a potentially more accurate framework for relativistic fluid dynamics.

Abstract

We re-derive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast to the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.