The evolution equation for the energy-momentum moments of the non-equilibrium density function & The regularized relativistic third order hydrodynamics

Abstract

In this work, we first derive the evolution equation for the general energy-momentum moment of $\delta f$, where $\delta f$ is the deviation from the local equilibrium phase space density. We then introduce a relativistic extension of regularized hydrodynamics developed in the non-relativistic case by Struchtrup and Torrilhon that combines the method of moments and Chapman-Enskog expansion. Hydrodynamic equations up to the third-order in gradients are then systematially derived within the context of a single species system and the relaxation time approximation. This is followed by a series of linear stability and causality analysis. For the system of massless particles without any charge conservation, the third-order hydrodynamics is shown to be linearly stable and causal.

37 pages with extensive appendices. 8 figures. Version accepted by Physical Review C

References in corpus (21)

• Chiral anomaly and local polarization effect from quantum kinetic approach
• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• Stability and Causality in relativistic dissipative hydrodynamics
• Stable and causal relativistic Navier-Stokes equations
• From Chiral Kinetic Theory To Relativistic Viscous Spin Hydrodynamics
• Non-dissipative second-order transport, spin, and pseudo-gauge transformations in hydrodynamics
• Nonlinear Constraints on Relativistic Fluids Far From Equilibrium
• Relativistic third-order viscous corrections to the entropy four-current from kinetic theory
• When the entropy has no maximum: A new perspective on the instability of the first-order theories of dissipation
• Relativistic first-order spin hydrodynamics via the Chapman-Enskog expansion
• Linear stability of Israel-Stewart theory in the presence of net-charge diffusion
• Fluctuating relativistic dissipative hydrodynamics as a gauge theory
• The causality and stability of relativistic spin-hydrodynamics
• Equivalence between first-order causal and stable hydrodynamics and Israel-Stewart theory for boost-invariant systems with a constant relaxation time
• On the linear causality and stability of third-order relativistic dissipative fluid dynamics
• Conformal Bjorken flow in the general frame and its attractor: Similarities and discrepancies with the Müller-Israel-Stewart formalism
• Relaxation-time approximation and relativistic third-order viscous hydrodynamics from kinetic theory
• Relativistic second-order viscous hydrodynamics from kinetic theory with extended relaxation-time approximation
• Causal third-order viscous hydrodynamics within relaxation-time approximation
• Third order viscous hydrodynamics from the entropy four current
• Causality and stability in first-order conformal anisotropic hydrodynamics