Relativistic hydrodynamics with momentum dependent relaxation time

TL;DR

This paper develops a second order relativistic hydrodynamic theory incorporating momentum dependent relaxation time, using Chapman-Enskog expansion, and compares it with other methods, revealing a fractional momentum dependence and establishing methodological equivalences.

Contribution

It introduces a relativistic hydrodynamic framework with momentum dependent relaxation time using Chapman-Enskog expansion, linking it to existing moment methods and numerical solutions.

Findings

Momentum dependent relaxation time extends Landau matching conditions.

Numerical solutions suggest fractional momentum dependence is appropriate.

An equivalence between Chapman-Enskog and Grad's 14-moment method is established.

Abstract

A second order relativistic hydrodynamic theory has been derived using momentum dependent relaxation time in the relativistic transport equation. In order to do that, an iterative technique of gradient expansion approach, namely Chapman-Enskog (CE) expansion of the particle distribution function has been employed. The key findings of this work are, (i) momentum dependent relaxation time in collision term results in an extended Landau matching condition for the thermodynamic variables, (ii) the result from numerical solution of Boltzmann equation lies somewhere in between the two popular extreme limits : linear and quadratic ansatz, indicating a fractional power of momentum dependence in relaxation time to be appropriate, (ii) an equivalence has been established between the iterative gradient expansion method like CE and the well known moment approach like Grad's 14-moment method.