Shear-bulk coupling in nonconformal hydrodynamics

TL;DR

This paper compares second-order viscous hydrodynamics and anisotropic hydrodynamics in modeling the evolution of pressure anisotropy and bulk pressure in a massive gas, emphasizing the importance of shear-bulk couplings for accuracy.

Contribution

It demonstrates that including shear-bulk couplings in second-order viscous hydrodynamics is essential for accurately describing bulk pressure evolution.

Findings

Shear-bulk couplings are crucial in second-order hydrodynamics.

Both hydrodynamic approaches can match the exact Boltzmann solution.

Anisotropic hydrodynamics performs comparably to enhanced second-order hydrodynamics.

Abstract

We compute the temporal evolution of the pressure anisotropy and bulk pressure of a massive gas using second-order viscous hydrodynamics and anisotropic hydrodynamics. We then compare our results with an exact solution of the Boltzmann equation for a massive gas in the relaxation time approximation. We demonstrate that, within second-order viscous hydrodynamics, the inclusion of the full set of kinetic coefficients, particularly the shear-bulk couplings, is necessary to properly describe the time evolution of the bulk pressure. We also compare the results of second-order hydrodynamics with those obtained using the anisotropic hydrodynamics approach. We find that anisotropic hydrodynamics and second-order viscous hydrodynamics including the shear-bulk couplings are both able to reproduce the exact evolution with comparable accuracy.