Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation

Abstract

We present an exact solution to the Boltzmann equation which describes a system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion for arbitrary shear viscosity to entropy density ratio. This new solution is constructed by considering the conformal map between Minkowski space and the direct product of three dimensional de Sitter space with a line. The resulting solution respects SO(3)_q x SO(1,1) x Z_2 symmetry. We compare the exact kinetic solution with exact solutions of the corresponding macroscopic equations that were obtained from the kinetic theory in ideal and second-order viscous hydrodynamic approximations. The macroscopic solutions are obtained in de Sitter space and are subject to the same symmetries used to obtain the exact kinetic solution.

37 pages, 10 figures; v1.1 of code is included as ancillary files; v3 - published version

References in corpus (12)

• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Dissipative Dynamics of Highly Anisotropic Systems
• Highly-anisotropic and strongly-dissipative hydrodynamics for early stages of relativistic heavy-ion collisions
• Global Classical Solutions of the Boltzmann Equation without Angular Cut-off
• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• Boost-Invariant (2+1)-dimensional Anisotropic Hydrodynamics
• A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit
• Origin of the Relaxation Time in Dissipative Fluid Dynamics
• Highly-anisotropic hydrodynamics in 3+1 space-time dimensions
• Non-boost-invariant motion of dissipative and highly anisotropic fluid
• Leading-order anisotropic hydrodynamics for systems with massive particles
• Hydrodynamics of anisotropic quark and gluon fluids

Cited by in corpus (18)

• Causality of the Einstein-Israel-Stewart Theory with Bulk Viscosity
• Bottomonium suppression using a lattice QCD vetted potential
• Analytical and numerical Gubser solutions of the second-order hydrodynamics
• Anisotropic hydrodynamics for conformal Gubser flow
• Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
• Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime
• Hydrodynamization and non-equilibrium Green's functions in kinetic theory
• Hydrodynamics from free-streaming to thermalization and back again
• Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons
• Exact solution of the (0+1)-dimensional Boltzmann equation for massive Bose-Einstein and Fermi-Dirac gases
• Non-boost-invariant dissipative hydrodynamics
• Anisotropic-hydrodynamics approach to a quark-gluon fluid mixture
• Analytic solutions of the relativistic Boltzmann equation
• Far-from-equilibrium kinetic dynamics of $\lambda {\varphi }^4$ theory in an expanding universe
• Determining Transport Coefficients for a Microscopic Simulation of a Hadron Gas
• Recent progress in anisotropic hydrodynamics
• Non-conformal evolution of magnetic fields during reheating
• Non-equilibrium hydrodynamics of the quark-gluon plasma