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

Denicol, Gabriel; Heinz, Ulrich; Martinez, Mauricio; Noronha, Jorge; Strickland, Michael

doi:10.1103/PhysRevD.90.125026

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

Journal Article · Wed Dec 24 00:00:00 EST 2014 · Physical Review. D, Particles, Fields, Gravitation and Cosmology

DOI:https://doi.org/10.1103/PhysRevD.90.125026· OSTI ID:1604537

Denicol, Gabriel ^[1]; ^[2]; Martinez, Mauricio ^[2]; Noronha, Jorge ^[3]; Strickland, Michael ^[4]

McGill Univ., Montreal, QC (Canada); The Ohio State University
The Ohio State Univ., Columbus, OH (United States)
Univ. de Sao Paulo (Brazil)
Kent State Univ., Kent, OH (United States)

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 $$SO(3)_q\otimes SO(1,1)\otimes Z_2$$ 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.

View Accepted Manuscript (DOE)

Research Organization:: The Ohio State Univ., Columbus, OH (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

Grant/Contract Number:: AC02-05CH11231; SC0004104; SC0004286

OSTI ID:: 1604537

Alternate ID(s):: OSTI ID: 1181197

Journal Information:: Physical Review. D, Particles, Fields, Gravitation and Cosmology, Journal Name: Physical Review. D, Particles, Fields, Gravitation and Cosmology Journal Issue: 12 Vol. 90; ISSN PRVDAQ; ISSN 1550-7998

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (60)

The Relativistic Boltzmann Equation: Theory and Applications Cercignani, Carlo; Kremer, Gilberto Medeiros Progress in Mathematical Physics, Vol. 22 https://doi.org/10.1007/978-3-0348-8165-4	book	January 2002
Transient relativistic thermodynamics and kinetic theory Israel, W.; Stewart, J. M. Annals of Physics, Vol. 118, Issue 2 https://doi.org/10.1016/0003-4916(79)90130-1	journal	April 1979
Stability and causality in dissipative relativistic fluids Hiscock, William A.; Lindblom, Lee Annals of Physics, Vol. 151, Issue 2 https://doi.org/10.1016/0003-4916(83)90288-9	journal	December 1983
A relativistic relaxation-time model for the Boltzmann equation Anderson, J. L.; Witting, H. R. Physica, Vol. 74, Issue 3 https://doi.org/10.1016/0031-8914(74)90355-3	journal	June 1974
Thermal equilibration in ultra-relativistic heavy-ion collisions Baym, Gordon Physics Letters B, Vol. 138, Issue 1-3 https://doi.org/10.1016/0370-2693(84)91863-X	journal	April 1984
Entropy production and the evolution of ultra-relativistic heavy ion collisions Baym, Gordon Nuclear Physics A, Vol. 418 https://doi.org/10.1016/0375-9474(84)90573-6	journal	April 1984
Oscillations of quark-gluon plasma generated in strong color fields Białas, A.; Czyż, W.; Dyrek, A. Nuclear Physics B, Vol. 296, Issue 3 https://doi.org/10.1016/0550-3213(88)90035-1	journal	January 1988
Dissipative dynamics of highly anisotropic systems Martinez, Mauricio; Strickland, Michael Nuclear Physics A, Vol. 848, Issue 1-2 https://doi.org/10.1016/j.nuclphysa.2010.08.011	journal	December 2010
Non-boost-invariant anisotropic dynamics Martinez, Mauricio; Strickland, Michael Nuclear Physics A, Vol. 856, Issue 1 https://doi.org/10.1016/j.nuclphysa.2011.02.003	journal	April 2011
Anisotropic hydrodynamics for rapidly expanding systems Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael Nuclear Physics A, Vol. 916 https://doi.org/10.1016/j.nuclphysa.2013.08.004	journal	October 2013
Conformal hydrodynamics in Minkowski and de Sitter spacetimes Gubser, Steven S.; Yarom, Amos Nuclear Physics B, Vol. 846, Issue 3 https://doi.org/10.1016/j.nuclphysb.2011.01.012	journal	May 2011
General relativistic Boltzmann equation, I: Covariant treatment Debbasch, F.; van Leeuwen, W. A. Physica A: Statistical Mechanics and its Applications, Vol. 388, Issue 7 https://doi.org/10.1016/j.physa.2008.12.023	journal	April 2009
General relativistic Boltzmann equation, II: Manifestly covariant treatment Debbasch, F.; van Leeuwen, W. A. Physica A: Statistical Mechanics and its Applications, Vol. 388, Issue 9 https://doi.org/10.1016/j.physa.2009.01.009	journal	May 2009
Non-boost-invariant motion of dissipative and highly anisotropic fluid Ryblewski, Radoslaw; Florkowski, Wojciech Journal of Physics G: Nuclear and Particle Physics, Vol. 38, Issue 1 https://doi.org/10.1088/0954-3899/38/1/015104	journal	December 2010
Relativistic viscous hydrodynamics, conformal invariance, and holography Baier, Rudolf; Romatschke, Paul; Son, Dam Thanh Journal of High Energy Physics, Vol. 2008, Issue 04 https://doi.org/10.1088/1126-6708/2008/04/100	journal	April 2008
Global classical solutions of the Boltzmann equation without angular cut-off Gressman, Philip T.; Strain, Robert M. Journal of the American Mathematical Society, Vol. 24, Issue 3 https://doi.org/10.1090/S0894-0347-2011-00697-8	journal	September 2011
A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems Bhatnagar, P. L.; Gross, E. P.; Krook, M. Physical Review, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRev.94.511	journal	May 1954
Extension of relativistic dissipative hydrodynamics to third order El, Andrej; Xu, Zhe; Greiner, Carsten Physical Review C, Vol. 81, Issue 4 https://doi.org/10.1103/PhysRevC.81.041901	journal	April 2010
Highly anisotropic and strongly dissipative hydrodynamics for early stages of relativistic heavy-ion collisions Florkowski, Wojciech; Ryblewski, Radoslaw Physical Review C, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevC.83.034907	journal	March 2011
Projection method for boost-invariant and cylindrically symmetric dissipative hydrodynamics Florkowski, Wojciech; Ryblewski, Radoslaw Physical Review C, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevC.85.044902	journal	April 2012
Highly anisotropic hydrodynamics in 3 + 1 space-time dimensions Ryblewski, Radoslaw; Florkowski, Wojciech Physical Review C, Vol. 85, Issue 6 https://doi.org/10.1103/PhysRevC.85.064901	journal	June 2012
Boost-invariant (2+1)-dimensional anisotropic hydrodynamics Martinez, Mauricio; Ryblewski, Radoslaw; Strickland, Michael Physical Review C, Vol. 85, Issue 6 https://doi.org/10.1103/PhysRevC.85.064913	journal	June 2012
Hydrodynamics of anisotropic quark and gluon fluids Florkowski, Wojciech; Maj, Radoslaw; Ryblewski, Radoslaw Physical Review C, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevC.87.034914	journal	March 2013
Relativistic dissipative hydrodynamics from kinetic theory with relaxation-time approximation Jaiswal, Amaresh Physical Review C, Vol. 87, Issue 5 https://doi.org/10.1103/PhysRevC.87.051901	journal	May 2013
Relativistic third-order dissipative fluid dynamics from kinetic theory Jaiswal, Amaresh Physical Review C, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevC.88.021903	journal	August 2013
Testing viscous and anisotropic hydrodynamics in an exactly solvable case Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael Physical Review C, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevC.88.024903	journal	August 2013
Projection method and new formulation of leading-order anisotropic hydrodynamics Tinti, Leonardo; Florkowski, Wojciech Physical Review C, Vol. 89, Issue 3 https://doi.org/10.1103/PhysRevC.89.034907	journal	March 2014
Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods Bhalerao, Rajeev S.; Jaiswal, Amaresh; Pal, Subrata Physical Review C, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevC.89.054903	journal	May 2014
Exact solution of the ( 0 + 1 )-dimensional Boltzmann equation for a massive gas Florkowski, Wojciech; Maksymiuk, Ewa; Ryblewski, Radoslaw Physical Review C, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevC.89.054908	journal	May 2014
Leading-order anisotropic hydrodynamics for systems with massive particles Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael Physical Review C, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevC.89.054909	journal	May 2014
Second-order ( 2 + 1 ) -dimensional anisotropic hydrodynamics Bazow, Dennis; Heinz, Ulrich; Strickland, Michael Physical Review C, Vol. 90, Issue 5 https://doi.org/10.1103/PhysRevC.90.054910	journal	November 2014
Highly relativistic nucleus-nucleus collisions: The central rapidity region Bjorken, J. D. Physical Review D, Vol. 27, Issue 1 https://doi.org/10.1103/PhysRevD.27.140	journal	January 1983
Boost-invariant Boltzmann-Vlasov equations for relativistic quark-antiquark plasma Białas, A.; Czyż, W. Physical Review D, Vol. 30, Issue 11 https://doi.org/10.1103/PhysRevD.30.2371	journal	December 1984
Generic instabilities in first-order dissipative relativistic fluid theories Hiscock, William A.; Lindblom, Lee Physical Review D, Vol. 31, Issue 4 https://doi.org/10.1103/PhysRevD.31.725	journal	February 1985
Symmetry constraints on generalizations of Bjorken flow Gubser, Steven S. Physical Review D, Vol. 82, Issue 8 https://doi.org/10.1103/PhysRevD.82.085027	journal	October 2010
Origin of the relaxation time in dissipative fluid dynamics Denicol, Gabriel S.; Noronha, Jorge; Niemi, Harri Physical Review D, Vol. 83, Issue 7 https://doi.org/10.1103/PhysRevD.83.074019	journal	April 2011
Derivation of transient relativistic fluid dynamics from the Boltzmann equation Denicol, G. S.; Niemi, H.; Molnár, E. Physical Review D, Vol. 85, Issue 11 https://doi.org/10.1103/PhysRevD.85.114047	journal	June 2012
Exact analytical solutions of second order conformal hydrodynamics Hatta, Yoshitaka; Noronha, Jorge; Xiao, Bo-Wen Physical Review D, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevD.89.051702	journal	March 2014
Systematic study of exact solutions in second-order conformal hydrodynamics Hatta, Yoshitaka; Noronha, Jorge; Xiao, Bo-Wen Physical Review D, Vol. 89, Issue 11 https://doi.org/10.1103/PhysRevD.89.114011	journal	June 2014
Dissipative Relativistic Fluid Dynamics: A New Way to Derive the Equations of Motion from Kinetic Theory Denicol, G. S.; Koide, T.; Rischke, D. H. Physical Review Letters, Vol. 105, Issue 16 https://doi.org/10.1103/PhysRevLett.105.162501	journal	October 2010
New Exact Solution of the Relativistic Boltzmann Equation and its Hydrodynamic Limit Denicol, Gabriel S.; Heinz, Ulrich; Martinez, Mauricio Physical Review Letters, Vol. 113, Issue 20 https://doi.org/10.1103/PhysRevLett.113.202301	journal	November 2014
Derivation of fluid dynamics from kinetic theory with the 14-moment approximation Denicol, G. S.; Molnár, E.; Niemi, H. The European Physical Journal A, Vol. 48, Issue 11 https://doi.org/10.1140/epja/i2012-12170-x	journal	November 2012
Highly anisotropic and strongly dissipative hydrodynamics with transverse expansion Ryblewski, Radoslaw; Florkowski, Wojciech The European Physical Journal C, Vol. 71, Issue 11 https://doi.org/10.1140/epjc/s10052-011-1761-8	journal	November 2011
Dissipative Dynamics of Highly Anisotropic Systems Martinez, Mauricio; Strickland, Michael arXiv https://doi.org/10.48550/arxiv.1007.0889	text	January 2010
Non-boost-invariant anisotropic dynamics Martinez, Mauricio; Strickland, Michael arXiv https://doi.org/10.48550/arxiv.1011.3056	text	January 2010
Global Classical Solutions of the Boltzmann Equation without Angular Cut-off Gressman, Philip T.; Strain, Robert M. arXiv https://doi.org/10.48550/arxiv.1011.5441	text	January 2010
Conformal hydrodynamics in Minkowski and de Sitter spacetimes Gubser, Steven S.; Yarom, Amos arXiv https://doi.org/10.48550/arxiv.1012.1314	text	January 2010
Origin of the Relaxation Time in Dissipative Fluid Dynamics Denicol, G. S.; Noronha, J.; Niemi, H. arXiv https://doi.org/10.48550/arxiv.1102.4780	text	January 2011
Derivation of transient relativistic fluid dynamics from the Boltzmann equation Denicol, G. S.; Niemi, H.; Molnar, E. arXiv https://doi.org/10.48550/arxiv.1202.4551	text	January 2012
Boost-Invariant (2+1)-dimensional Anisotropic Hydrodynamics Martinez, Mauricio; Ryblewski, Radoslaw; Strickland, Michael arXiv https://doi.org/10.48550/arxiv.1204.1473	text	January 2012
Highly-anisotropic hydrodynamics in 3+1 space-time dimensions Ryblewski, Radoslaw; Florkowski, Wojciech arXiv https://doi.org/10.48550/arxiv.1204.2624	text	January 2012
Hydrodynamics of anisotropic quark and gluon fluids Florkowski, Wojciech; Maj, Radoslaw; Ryblewski, Radoslaw arXiv https://doi.org/10.48550/arxiv.1209.3671	text	January 2012
Mixture of anisotropic fluids Florkowski, Wojciech; Maj, Radoslaw arXiv https://doi.org/10.48550/arxiv.1309.2786	text	January 2013
Second-order (2+1)-dimensional anisotropic hydrodynamics Bazow, Dennis; Heinz, Ulrich W.; Strickland, Michael arXiv https://doi.org/10.48550/arxiv.1311.6720	text	January 2013
Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods Bhalerao, Rajeev S.; Jaiswal, Amaresh; Pal, Subrata arXiv https://doi.org/10.48550/arxiv.1312.1864	text	January 2013
Projection method and new formulation of leading-order anisotropic hydrodynamics Tinti, Leonardo; Florkowski, Wojciech arXiv https://doi.org/10.48550/arxiv.1312.6614	text	January 2013
Exact analytical solutions of second-order conformal hydrodynamics Hatta, Yoshitaka; Noronha, Jorge; Xiao, Bo-Wen arXiv https://doi.org/10.48550/arxiv.1401.6248	text	January 2014
Kinetic description of mixtures of anisotropic fluids Florkowski, Wojciech; Madetko, Oskar arXiv https://doi.org/10.48550/arxiv.1402.2401	text	January 2014
Mixture of Anisotropic Fluids Florkowski, W.; Maj, R. Acta Physica Polonica B, Vol. 44, Issue 10 https://doi.org/10.5506/APhysPolB.44.2003	journal	January 2013
Kinetic Description of Mixtures of Anisotropic Fluids Florkowski, W.; Madetko, O. Acta Physica Polonica B, Vol. 45, Issue 5 https://doi.org/10.5506/APhysPolB.45.1103	journal	January 2014

Cited By (27)

Anderson–Witting Model of the Relativistic Boltzmann Equation Near Equilibrium Hwang, Byung-Hoon; Yun, Seok-Bae Journal of Statistical Physics, Vol. 176, Issue 4 https://doi.org/10.1007/s10955-019-02330-3	journal	June 2019
New theories of relativistic hydrodynamics in the LHC era Florkowski, Wojciech; Heller, Michal P.; Spaliński, Michał Reports on Progress in Physics, Vol. 81, Issue 4 https://doi.org/10.1088/1361-6633/aaa091	journal	February 2018
Exploring the applicability of dissipative fluid dynamics to small systems by comparison to the Boltzmann equation Gallmeister, K.; Niemi, H.; Greiner, C. Physical Review C, Vol. 98, Issue 2 https://doi.org/10.1103/physrevc.98.024912	journal	August 2018
Effective kinetic description of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions Kurkela, Aleksi; Mazeliauskas, Aleksas; Paquet, Jean-François Physical Review C, Vol. 99, Issue 3 https://doi.org/10.1103/physrevc.99.034910	journal	March 2019
Entropy production, hydrodynamics, and resurgence in the primordial quark-gluon plasma from holography Buchel, Alex; Heller, Michal P.; Noronha, Jorge Physical Review D, Vol. 94, Issue 10 https://doi.org/10.1103/physrevd.94.106011	journal	November 2016
Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime Bazow, D.; Denicol, G. S.; Heinz, U. Physical Review D, Vol. 94, Issue 12 https://doi.org/10.1103/physrevd.94.125006	journal	December 2016
Bottomonium suppression using a lattice QCD vetted potential Krouppa, Brandon; Rothkopf, Alexander; Strickland, Michael Physical Review D, Vol. 97, Issue 1 https://doi.org/10.1103/physrevd.97.016017	journal	January 2018
Anisotropic nonequilibrium hydrodynamic attractor Strickland, Michael; Noronha, Jorge; Denicol, Gabriel S. Physical Review D, Vol. 97, Issue 3 https://doi.org/10.1103/physrevd.97.036020	journal	February 2018
Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M. Physical Review D, Vol. 97, Issue 4 https://doi.org/10.1103/physrevd.97.044041	journal	February 2018
Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics Denicol, Gabriel S.; Noronha, Jorge Physical Review D, Vol. 97, Issue 5 https://doi.org/10.1103/physrevd.97.056021	journal	March 2018
How does relativistic kinetic theory remember about initial conditions? Heller, Michal P.; Svensson, Viktor Physical Review D, Vol. 98, Issue 5 https://doi.org/10.1103/physrevd.98.054016	journal	September 2018
Causality and existence of solutions of relativistic viscous fluid dynamics with gravity Bemfica, Fábio S.; Disconzi, Marcelo M.; Noronha, Jorge Physical Review D, Vol. 98, Issue 10 https://doi.org/10.1103/physrevd.98.104064	journal	November 2018
Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow Denicol, Gabriel S.; Noronha, Jorge Physical Review D, Vol. 99, Issue 11 https://doi.org/10.1103/physrevd.99.116004	journal	June 2019
Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow Behtash, Alireza; Kamata, Syo; Martinez, Mauricio Physical Review D, Vol. 99, Issue 11 https://doi.org/10.1103/physrevd.99.116012	journal	June 2019
Importance of the Bulk Viscosity of QCD in Ultrarelativistic Heavy-Ion Collisions Ryu, S.; Paquet, J. -F.; Shen, C. Physical Review Letters, Vol. 115, Issue 13 https://doi.org/10.1103/physrevlett.115.132301	journal	September 2015
Analytic Solution of the Boltzmann Equation in an Expanding System Bazow, D.; Denicol, G. S.; Heinz, U. Physical Review Letters, Vol. 116, Issue 2 https://doi.org/10.1103/physrevlett.116.022301	journal	January 2016
Strongly coupled quark-gluon plasma in heavy ion collisions Shuryak, Edward Reviews of Modern Physics, Vol. 89, Issue 3 https://doi.org/10.1103/revmodphys.89.035001	journal	July 2017
A study of vorticity formation in high energy nuclear collisions Becattini, F.; Inghirami, G.; Rolando, V. The European Physical Journal C, Vol. 75, Issue 9 https://doi.org/10.1140/epjc/s10052-015-3624-1	journal	September 2015
Collective classical motion on hyperbolic spacetimes of any dimensions Cotăescu, Ion I. Modern Physics Letters A, Vol. 34, Issue 21 https://doi.org/10.1142/s0217732319501657	journal	July 2019
Introduction to hydrodynamics Jeon, Sangyong; Heinz, Ulrich International Journal of Modern Physics E, Vol. 24, Issue 10 https://doi.org/10.1142/s0218301315300106	journal	October 2015
The importance of the bulk viscosity of QCD in ultrarelativistic heavy-ion collisions Ryu, S.; Paquet, J. -F.; Shen, C. arXiv https://doi.org/10.48550/arxiv.1502.01675	text	January 2015
Entropy Production, Hydrodynamics, and Resurgence in the Primordial Quark-Gluon Plasma from Holography Buchel, Alex; Heller, Michal P.; Noronha, Jorge arXiv https://doi.org/10.48550/arxiv.1603.05344	text	January 2016
Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime Bazow, D.; Denicol, G. S.; Heinz, U. arXiv https://doi.org/10.48550/arxiv.1607.05245	text	January 2016
Causality and existence of solutions of relativistic viscous fluid dynamics with gravity Bemfica, Fabio S.; Disconzi, Marcelo M.; Noronha, Jorge arXiv https://doi.org/10.48550/arxiv.1708.06255	text	January 2017
Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics Denicol, Gabriel S.; Noronha, Jorge arXiv https://doi.org/10.48550/arxiv.1711.01657	text	January 2017
Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M. arXiv https://doi.org/10.48550/arxiv.1711.01745	text	January 2017
Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow Denicol, Gabriel; Noronha, Jorge arXiv https://doi.org/10.48550/arxiv.1804.04771	text	January 2018

Similar Records

Nonconformal viscous anisotropic hydrodynamics

Journal Article · Wed Jun 03 20:00:00 EDT 2015 · Physical Review C, Nuclear Physics · OSTI ID:1604532

New Exact Solution of the Relativistic Boltzmann Equation and its Hydrodynamic Limit

Journal Article · Thu Nov 13 19:00:00 EST 2014 · Physical Review Letters · OSTI ID:1604538

Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions

Journal Article · Tue Jun 07 20:00:00 EDT 2016 · Nuclear and Particle Physics Proceedings · OSTI ID:1604416

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

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

Citation Formats

References (60)

Cited By (27)

Similar Records

Related Subjects