Bulk viscosity and $n$-component fluids

TL;DR

This paper develops a second-order hydrodynamic framework for n-component relativistic fluids with small chemical potentials, providing explicit evolution equations and transport coefficients relevant for dense viscous systems like neutron star mergers.

Contribution

It introduces a method to diagonalize evolution equations for chemical potentials and derives explicit bulk scalar evolution equations for multi-component fluids.

Findings

Derived explicit evolution equations for bulk scalar in n-component fluids.

Identified 2n transport quantities governing the system.

Established a Green's function framework for the fluid in the rest frame.

Abstract

Understanding the hydrodynamics of out-of-equilibrium dense viscous fluids is of key importance to accurate descriptions of physical systems such as compact stars, particularly their mergers. We consider a near-equilibrium relativistic fluid with $n$ independent and small chemical potentials restoring the system back towards equilibrium. By diagonalising the evolution equation for the out-of-equilibrium chemical potentials, we construct an explicit evolution equation for the bulk scalar of the system in second-order hydrodynamics in terms of equilibrium quantities. We find expressions for the $2n$ transport quantities and show that in the rest frame of the fluid, the system admits a Green's function corresponding to an $n$-component fluid.