Acausality-driven instabilities in transient relativistic viscous hydrodynamics

Abstract

We investigate non-linear instabilities stemming from superluminal propagation of information in Israel-Stewart-like models of relativistic viscous fluid dynamics. In relativity, the characteristic speed of propagation of information, $w$, and the speed of the fluid, $v$, allow us to differentiate between regimes of the hydrodynamic equations that are acausal but stable ($w>1$), unstable ($v^2{w}^2\ge 1$), and covariantly ill-posed ($w^2\le 0$). As an analytical benchmark, we present a new solution that illustrates these distinct regimes. We compare this analytical solution to the result of a numerical relativistic viscous fluid dynamics solver, and confirm that the analytical result can be recovered numerically in the stable regime, whether causal or acausal. The onset of numerical instabilities is further found to occur in the regime predicted by the analytical solution.

16 pages, 6 figures -- v2 after peer-review version

References in corpus (31)

• Nonlinear Fluid Dynamics from Gravity
• The equation of state in (2+1)-flavor QCD
• Causality, Analyticity and an IR Obstruction to UV Completion
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics
• Hydrodynamic Modeling of Heavy-Ion Collisions
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• Fluctuating Glasma initial conditions and flow in heavy ion collisions
• 3+1D hydrodynamic simulation of relativistic heavy-ion collisions
• k-Essence, superluminal propagation, causality and emergent geometry
• The production of photons in relativistic heavy-ion collisions
• Event-by-event gluon multiplicity, energy density and eccentricities at RHIC and LHC
• First-order relativistic hydrodynamics is stable
• Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
• Bayesian analysis of heavy ion collisions with the heavy ion computational framework Trajectum
• Nonlinear causality of general first-order relativistic viscous hydrodynamics
• Does stability of relativistic dissipative fluid dynamics imply causality?
• Transport Coefficients of Bulk Viscous Pressure in the 14-moment approximation
• Running the gamut of high energy nuclear collisions
• Hydrodynamic Approaches in Relativistic Heavy Ion Reactions
• Causality of the Einstein-Israel-Stewart Theory with Bulk Viscosity
• Nonlinear Constraints on Relativistic Fluids Far From Equilibrium
• Numerical tests of causal relativistic dissipative fluid dynamics
• Theories of Relativistic Dissipative Fluid Dynamics
• Causality violations in realistic simulations of heavy-ion collisions
• Exploring theoretical uncertainties in the hydrodynamic description of relativistic heavy-ion collisions
• Inverse-Reynolds-Dominance approach to transient fluid dynamics
• Dispersion relations alone cannot guarantee causality
• Is Relativistic Hydrodynamics always Symmetric-Hyperbolic in the Linear Regime?
• Causality violations in simulations of large and small heavy-ion collisions
• The relativistic Euler equations: Remarkable null structures and regularity properties

Cited by in corpus (1)

• Relativistic Dispersion Spectra across Lorentz boosted frames: Spurious modes and the enigma of causality