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.

arXiv comment37 pages, 10 figures; v1.1 of code is included as ancillary files; v3 - published version

References in corpus (33)

• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• 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
• Symmetry constraints on generalizations of Bjorken flow
• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• Global Strong Solutions of the Boltzmann Equation without Angular Cut-off
• Testing viscous and anisotropic hydrodynamics in an exactly solvable case
• Conformal hydrodynamics in Minkowski and de Sitter spacetimes
• Boost-Invariant (2+1)-dimensional Anisotropic Hydrodynamics
• Anisotropic Hydrodynamics for Rapidly Expanding Systems
• Relativistic third-order dissipative fluid dynamics from kinetic theory
• Second-order (2+1)-dimensional anisotropic hydrodynamics
• A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit
• Third-order relativistic dissipative hydrodynamics
• Origin of the Relaxation Time in Dissipative Fluid Dynamics
• Highly-anisotropic hydrodynamics in 3+1 space-time dimensions
• Relativistic dissipative hydrodynamics from kinetic theory with relaxation time approximation
• Derivation of fluid dynamics from kinetic theory with the 14--moment approximation
• Non-boost-invariant anisotropic dynamics
• Exact solution of the (0+1)-dimensional Boltzmann equation for a massive gas
• Non-boost-invariant motion of dissipative and highly anisotropic fluid
• Projection method and new formulation of leading-order anisotropic hydrodynamics
• Highly-anisotropic and strongly-dissipative hydrodynamics with transverse expansion
• Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods
• Leading-order anisotropic hydrodynamics for systems with massive particles
• Hydrodynamics of anisotropic quark and gluon fluids
• Projection method for boost-invariant and cylindrically symmetric dissipative hydrodynamics
• Exact analytical solutions of second-order conformal hydrodynamics
• A systematic study of exact solutions in second-order conformal hydrodynamics
• Mixture of anisotropic fluids
• Kinetic description of mixtures of anisotropic fluids

Cited by in corpus (90)

• The importance of the bulk viscosity of QCD in ultrarelativistic heavy-ion collisions
• New theories of relativistic hydrodynamics in the LHC era
• Heavy Ion Collisions: Achievements and Challenges
• Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
• A study of vorticity formation in high energy nuclear collisions
• Effective kinetic description of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions
• The anisotropic non-equilibrium hydrodynamic attractor
• Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow
• Entropy Production, Hydrodynamics, and Resurgence in the Primordial Quark-Gluon Plasma from Holography
• Relativistic anisotropic hydrodynamics
• The non-equilibrium attractor for kinetic theory in relaxation time approximation
• Causality of the Einstein-Israel-Stewart Theory with Bulk Viscosity
• Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation
• Bottomonium suppression in an open quantum system using the quantum trajectories method
• 3+1d quasiparticle anisotropic hydrodynamics for ultrarelativistic heavy-ion collisions
• Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics
• Bottomonium suppression using a lattice QCD vetted potential
• Analytical and numerical Gubser solutions of the second-order hydrodynamics
• How does relativistic kinetic theory remember about initial conditions?
• Exact hydrodynamic attractor of an ultrarelativistic gas of hard spheres
• The Present and Future of QCD
• Analytic solution of the Boltzmann equation in an expanding system
• Anisotropic hydrodynamics for conformal Gubser flow
• Anisotropic hydrodynamic modeling of 2.76 TeV Pb-Pb collisions
• Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow
• Bottomonium production in heavy-ion collisions using quantum trajectories: Differential observables and momentum anisotropy
• Quasiparticle equation of state for anisotropic hydrodynamics
• 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
• Leading-order anisotropic hydrodynamics for central collisions
• Coupled kinetic equations for quarks and gluons in the relaxation time approximation
• Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma
• Non-conformal attractor in boost-invariant plasmas
• Hydrodynamization and non-equilibrium Green's functions in kinetic theory
• On non-conformal kinetic theory and hydrodynamics for Bjorken flow
• Anisotropic fluid dynamics for Gubser flow
• Establishing the Range of Applicability of Hydrodynamics in High-Energy Collisions
• Quasiparticle anisotropic hydrodynamics for central collisions
• Hydrodynamics from free-streaming to thermalization and back again
• Photon production from a non-equilibrium quark-gluon plasma
• On higher order and anisotropic hydrodynamics for Bjorken and Gubser flows
• Dilepton production from the quark-gluon plasma using (3+1)-dimensional anisotropic dissipative hydrodynamics
• Photons from the Early Stages of Relativistic Heavy Ion Collisions
• Hydrodynamic attractors for Gubser flow
• Anisotropic hydrodynamic modeling of 200 GeV Au-Au collisions
• Extended relaxation time approximation and relativistic dissipative hydrodynamics
• Perturbative approaches in relativistic kinetic theory and the emergence of first-order hydrodynamics
• Global flow structure and exact formal transseries of the Gubser flow in kinetic theory
• Anisotropic hydrodynamics for conformal Gubser flow
• Bulk observables at 5.02 TeV using quasiparticle anisotropic hydrodynamics
• Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons
• A hydrodynamic approach to boost invariant free streaming
• Anisotropic hydrodynamics for mixture of quark and gluon fluids
• Exact solution of the (0+1)-dimensional Boltzmann equation for massive Bose-Einstein and Fermi-Dirac gases
• Testing different formulations of leading-order anisotropic hydrodynamics
• Anisotropic fluid dynamical simulations of heavy-ion collisions
• Exploring the applicability of dissipative fluid dynamics to small systems by comparison to the Boltzmann equation
• The regime of applicability of Israel-Stewart hydrodynamics
• Resummed hydrodynamic expansion for a plasma of particles interacting with fields
• Non-boost-invariant dissipative hydrodynamics
• Anisotropic-hydrodynamics approach to a quark-gluon fluid mixture
• Analytic solutions of the relativistic Boltzmann equation
• Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in ${\mathrm{AdS}}_2\otimes {\mathrm{S}}_2$
• Connecting far-from-equilibrium hydrodynamics to resummed transport coefficients and attractors
• Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation
• Far-from-equilibrium kinetic dynamics of $\lambda {\varphi }^4$ theory in an expanding universe
• Introduction to Hydrodynamics
• Anderson-Witting model of the relativistic Boltzmann equation near equilibrium
• Revisiting shear stress tensor evolution: Non-resistive magnetohydrodynamics with momentum-dependent relaxation time
• Investigating the domain of validity of the Gubser solution to the Boltzmann equation
• Determining Transport Coefficients for a Microscopic Simulation of a Hadron Gas
• High-order Shakhov-like extension of the relaxation time approximation in relativistic kinetic theory
• How Gubser flow ends in a holographic conformal theory
• Holographic Gubser flow: A combined analytic and numerical study
• Recent progress in anisotropic hydrodynamics
• Thermal dilepton production within conformal viscous Gubser flow
• Analytical Solution of the Nonlinear Relativistic Boltzmann Equation
• The onset of fluid-dynamical behavior in relativistic kinetic theory
• Non-conformal evolution of magnetic fields during reheating
• Maximally Symmetric Boost-Invariant Solutions of the Boltzmann Equation in Foliated Geometries
• Viscous anisotropic hydrodynamics for the Gubser flow
• Far-from-equilibrium hydrodynamic simulations of ultrarelativistic nuclear collisions
• Dissipative type theories for Bjorken and Gubser flows
• Finite-Density Dynamics of Chemically Equilibrating QGP in Conformal Gubser Flow and Hard Thermal Photon Production
• Kinetic equations and anisotropic hydrodynamics for quark and gluon fluids
• Production of $\psi (4040)$, $\psi (4160)$, and $\psi (4415)$ mesons in strong interactions
• Non-equilibrium hydrodynamics of the quark-gluon plasma
• Hot Spaghetti: Viscous Gravitational Collapse
• Extended applicability domain of viscous anisotropic hydrodynamics in (2+1)-D Bjorken flow with transverse expansion
• Collective classical motion on hyperbolic spacetimes of any dimensions