Skip to main content
SpringerLink
Log in

Bulk viscosity and cavitation in boost-invariant hydrodynamic expansion

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We solve second order relativistic hydrodynamics equations for a boost-invariant 1+1-dimensional expanding fluid with an equation of state taken from lattice calculations of the thermodynamics of strongly coupled quark-gluon plasma. We investigate the dependence of the energy density as a function of proper time on the values of the shear viscosity η, the bulk viscosity ζ, and second order coefficients, confirming that large changes in the values of the latter have negligible effects. Varying the shear viscosity between zero and a few times s/4π, with s the entropy density, has significant effects, as expected based on other studies. Introducing a nonzero bulk viscosity also has significant effects. In fact, if the bulk viscosity peaks near the crossover temperature T c to the degree indicated by recent lattice calculations in QCD without quarks, it can make the fluid cavitate — falling apart into droplets. It is interesting to see a hydrodynamic calculation predicting its own breakdown, via cavitation, at the temperatures where hadronization is thought to occur in ultrarelativistic heavy ion collisions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. PHENIX collaboration, K. Adcox et al., Formation of dense partonic matter in relativistic nucleus nucleus collisions at RHIC: experimental evaluation by the PHENIX collaboration, Nucl. Phys. A 757 (2005) 184 [nucl-ex/0410003] [SPIRES].

    ADS  Google Scholar 

  2. B.B. Back et al., The PHOBOS perspective on discoveries at RHIC, Nucl. Phys. A 757 (2005) 28 [nucl-ex/0410022] [SPIRES].

    ADS  Google Scholar 

  3. BRAHMS collaboration, I. Arsene et al., Quark gluon plasma an color glass condensate at RHIC? The perspective from the BRAHMS experiment, Nucl. Phys. A 757 (2005) 1 [nucl-ex/0410020] [SPIRES].

    ADS  Google Scholar 

  4. STAR collaboration, J. Adams et al., Experimental and theoretical challenges in the search for the quark gluon plasma: the STAR collaboration’s critical assessment of the evidence from RHIC collisions, Nucl. Phys. A 757 (2005) 102 [nucl-ex/0501009] [SPIRES].

    ADS  Google Scholar 

  5. PHOBOS collaboration, B. Alver et al., System size, energy, pseudorapidity and centrality dependence of elliptic flow, Phys. Rev. Lett. 98 (2007) 242302 [nucl-ex/0610037] [SPIRES].

    Article  ADS  Google Scholar 

  6. STAR collaboration, B.I. Abelev et al., Centrality dependence of charged hadron and strange hadron elliptic flow from \( \sqrt {{s_{\text{NN}}}} = 200\;GeV\;Au + Au \) collisions, Phys. Rev. C 77 (2008) 054901 [arXiv:0801.3466] [SPIRES].

    ADS  Google Scholar 

  7. J.-Y. Ollitrault, A.M. Poskanzer and S.A. Voloshin, Effect of flow fluctuations and nonflow on elliptic flow methods, Phys. Rev. C 80 (2009) 014904 [arXiv:0904.2315] [SPIRES].

    ADS  Google Scholar 

  8. P. Sorensen, Elliptic flow: a study of space-momentum correlations in relativistic nuclear collisions, arXiv:0905.0174 [SPIRES].

  9. R. Baier and P. Romatschke, Causal viscous hydrodynamics for central heavy-ion collisions, Eur. Phys. J. C 51 (2007) 677 [nucl-th/0610108] [SPIRES].

    Article  ADS  Google Scholar 

  10. P. Romatschke and U. Romatschke, Viscosity information from relativistic nuclear collisions: how perfect is the fluid observed at RHIC?, Phys. Rev. Lett. 99 (2007) 172301 [arXiv:0706.1522] [SPIRES].

    Article  ADS  Google Scholar 

  11. H. Song and U.W. Heinz, Suppression of elliptic flow in a minimally viscous quark-gluon plasma, Phys. Lett. B 658 (2008) 279 [arXiv:0709.0742] [SPIRES].

    ADS  Google Scholar 

  12. K. Dusling and D. Teaney, Simulating elliptic flow with viscous hydrodynamics, Phys. Rev. C 77 (2008) 034905 [arXiv:0710.5932] [SPIRES].

    ADS  Google Scholar 

  13. H. Song and U.W. Heinz, Causal viscous hydrodynamics in 2 + 1 dimensions for relativistic heavy-ion collisions, Phys. Rev. C 77 (2008) 064901 [arXiv:0712.3715] [SPIRES].

    ADS  Google Scholar 

  14. M. Luzum and P. Romatschke, Conformal relativistic viscous hydrodynamics: applications to RHIC results at \( \sqrt {{s_{\text{NN}}}} = 200\;GeV \), Phys. Rev. C 78 (2008) 034915 [Erratum ibid. C 79 (2009) 039903] [arXiv:0804.4015] [SPIRES].

    ADS  Google Scholar 

  15. H. Song and U.W. Heinz, Multiplicity scaling in ideal and viscous hydrodynamics, Phys. Rev. C 78 (2008) 024902 [arXiv:0805.1756] [SPIRES].

    ADS  Google Scholar 

  16. D. Molnar and P. Huovinen, Dissipative effects from transport and viscous hydrodynamics, J. Phys. G 35 (2008) 104125 [arXiv:0806.1367] [SPIRES].

    ADS  Google Scholar 

  17. H. Song and U.W. Heinz, Extracting the QGP viscosity from RHIC data — a status report from viscous hydrodynamics, J. Phys. G 36 (2009) 064033 [arXiv:0812.4274] [SPIRES].

    ADS  Google Scholar 

  18. M. Luzum and P. Romatschke, Viscous hydrodynamic predictions for nuclear collisions at the LHC, Phys. Rev. Lett. 103 (2009) 262302 [arXiv:0901.4588] [SPIRES].

    Article  Google Scholar 

  19. H. Song and U.W. Heinz, Viscous hydrodynamics with bulk viscosity — uncertainties from relaxation time and initial conditions, Nucl. Phys. A 830 (2009) 467c [arXiv:0907.2262] [SPIRES].

    Google Scholar 

  20. U.W. Heinz, Early collective expansion: relativistic hydrodynamics and the transport properties of QCD matter, arXiv:0901.4355 [SPIRES].

  21. P. Romatschke, New developments in relativistic viscous hydrodynamics, arXiv:0902.3663 [SPIRES].

  22. D.A. Teaney, Viscous hydrodynamics and the quark gluon plasma, arXiv:0905.2433 [SPIRES].

  23. D. Teaney, Effect of shear viscosity on spectra, elliptic flow and Hanbury Brown-Twiss radii, Phys. Rev. C 68 (2003) 034913 [nucl-th/0301099] [SPIRES].

    ADS  Google Scholar 

  24. G. Policastro, D.T. Son and A.O. Starinets, The shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [SPIRES].

    Article  ADS  Google Scholar 

  25. P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  26. A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [SPIRES].

    Article  ADS  Google Scholar 

  27. F. Cooper and G. Frye, Comment on the single particle distribution in the hydrodynamic and statistical thermodynamic models of multiparticle production, Phys. Rev. D 10 (1974) 186 [SPIRES].

    ADS  Google Scholar 

  28. S.A. Bass and A. Dumitru, Dynamics of hot bulk QCD matter: from the quark-gluon plasma to hadronic freeze-out, Phys. Rev. C 61 (2000) 064909 [nucl-th/0001033] [SPIRES].

    ADS  Google Scholar 

  29. D. Teaney, J. Lauret and E.V. Shuryak, A hydrodynamic description of heavy ion collisions at the SPS and RHIC, Phys. Rev. Lett. 86 (2001) 4783 [nucl-th/0110037] [SPIRES].

    Article  ADS  Google Scholar 

  30. C.E. Brennen, Cavitation and bubble dynamics, Oxford University Press, New York U.S.A. (1995).

    Google Scholar 

  31. J.D. Bjorken, Highly relativistic nucleus-nucleus collisions: the central rapidity region, Phys. Rev. D 27 (1983) 140 [SPIRES].

    ADS  Google Scholar 

  32. M. Prakash, M. Prakash, R. Venugopalan and G.M. Welke, How fast is equilibration in hot hadronic matter?, Phys. Rev. Lett. 70 (1993) 1228 [Nucl. Phys. A 566 (1994) 403C] [SPIRES].

    Article  ADS  Google Scholar 

  33. M. Prakash, M. Prakash, R. Venugopalan and G. Welke, Nonequilibrium properties of hadronic mixtures, Phys. Rept. 227 (1993) 321 [SPIRES].

    Article  ADS  Google Scholar 

  34. D. Davesne, Transport coefficients of a hot pion gas, Phys. Rev. C 53 (1996) 3069 [SPIRES].

    ADS  Google Scholar 

  35. A. Dobado and F.J. Llanes-Estrada, The viscosity of meson matter, Phys. Rev. D 69 (2004) 116004 [hep-ph/0309324] [SPIRES].

    ADS  Google Scholar 

  36. J.-W. Chen and E. Nakano, Shear viscosity to entropy density ratio of QCD below the deconfinement temperature, Phys. Lett. B 647 (2007) 371 [hep-ph/0604138] [SPIRES].

    ADS  Google Scholar 

  37. N. Demir and S.A. Bass, Shear-viscosity to entropy-density ratio of a relativistic hadron gas, Phys. Rev. Lett. 102 (2009) 172302 [arXiv:0812.2422] [SPIRES].

    Article  ADS  Google Scholar 

  38. N. Demir and S.A. Bass, η/s of a relativistic hadron gas at RHIC: approaching the AdS/CFT bound?, Nucl. Phys. A 830 (2009) 733c [arXiv:0907.4333] [SPIRES].

    Google Scholar 

  39. K. Paech and S. Pratt, Origins of bulk viscosity at RHIC, Phys. Rev. C 74 (2006) 014901 [nucl-th/0604008] [SPIRES].

    ADS  Google Scholar 

  40. D. Kharzeev and K. Tuchin, Bulk viscosity of QCD matter near the critical temperature, JHEP 09 (2008) 093 [arXiv:0705.4280] [SPIRES].

    Article  ADS  Google Scholar 

  41. H.B. Meyer, A calculation of the bulk viscosity in SU(3) gluodynamics, Phys. Rev. Lett. 100 (2008) 162001 [arXiv:0710.3717] [SPIRES].

    Article  ADS  Google Scholar 

  42. F. Karsch, D. Kharzeev and K. Tuchin, Universal properties of bulk viscosity near the QCD phase transition, Phys. Lett. B 663 (2008) 217 [arXiv:0711.0914] [SPIRES].

    ADS  Google Scholar 

  43. C. Sasaki and K. Redlich, Bulk viscosity in quasi particle models, Phys. Rev. C 79 (2009) 055207 [arXiv:0806.4745] [SPIRES].

    ADS  Google Scholar 

  44. H.B. Meyer, Transport properties of the quark-gluon plasma from lattice QCD, Nucl. Phys. A 830 (2009) 641c [arXiv:0907.4095] [SPIRES].

    Google Scholar 

  45. A. Muronga, Second order dissipative fluid dynamics for ultra-relativistic nuclear collisions, Phys. Rev. Lett. 88 (2002) 062302 [Erratum ibid. 89 (2002) 159901] [nucl-th/0104064] [SPIRES].

    Article  ADS  Google Scholar 

  46. A. Muronga, Causal theories of dissipative relativistic fluid dynamics for nuclear collisions, Phys. Rev. C 69 (2004) 034903 [nucl-th/0309055] [SPIRES].

    ADS  Google Scholar 

  47. A. Muronga and D.H. Rischke, Evolution of hot, dissipative quark matter in relativistic nuclear collisions, nucl-th/0407114 [SPIRES].

  48. U.W. Heinz, H. Song and A.K. Chaudhuri, Dissipative hydrodynamics for viscous relativistic fluids, Phys. Rev. C 73 (2006) 034904 [nucl-th/0510014] [SPIRES].

    ADS  Google Scholar 

  49. R. Baier, P. Romatschke and U.A. Wiedemann, Dissipative hydrodynamics and heavy ion collisions, Phys. Rev. C 73 (2006) 064903 [hep-ph/0602249] [SPIRES].

    ADS  Google Scholar 

  50. R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  51. R.J. Fries, B. Müller and A. Schafer, Stress tensor and bulk viscosity in relativistic nuclear collisions, Phys. Rev. C 78 (2008) 034913 [arXiv:0807.4333] [SPIRES].

    ADS  Google Scholar 

  52. M. Martinez and M. Strickland, Constraining relativistic viscous hydrodynamical evolution, Phys. Rev. C 79 (2009) 044903 [arXiv:0902.3834] [SPIRES].

    ADS  Google Scholar 

  53. G. Torrieri, B. Tomasik and I. Mishustin, Bulk viscosity driven clusterization of quark-gluon plasma and early freeze-out in relativistic heavy-ion collisions, Phys. Rev. C 77 (2008) 034903 [arXiv:0707.4405] [SPIRES].

    ADS  Google Scholar 

  54. G. Torrieri, B. Tomasik and I. Mishustin, Freeze-out by bulk viscosity driven instabilities, Acta Phys. Polon. B 39 (2008) 1733 [arXiv:0803.4070] [SPIRES].

    ADS  Google Scholar 

  55. G. Torrieri and I. Mishustin, Instability of boost-invariant hydrodynamics with a QCD inspired bulk viscosity, Phys. Rev. C 78 (2008) 021901 [arXiv:0805.0442] [SPIRES].

    ADS  Google Scholar 

  56. H. Kouno, M. Maruyama, F. Takagi and K. Saito, Relativistic hydrodynamics of quark-gluon plasma and stability of scaling solutions, Phys. Rev. D 41 (1990) 2903 [SPIRES=].

    ADS  Google Scholar 

  57. G.S. Denicol, T. Kodama, T. Koide and P. Mota, Effect of bulk viscosity on elliptic flow near QCD phase transition, Phys. Rev. C 80 (2009) 064901 [arXiv:0903.3595] [SPIRES].

    Google Scholar 

  58. G.S. Denicol, T. Kodama, T. Koide and P. Mota, Bulk viscosity effects on elliptic flow, Nucl. Phys. A 830 (2009) 729c [arXiv:0907.4269] [SPIRES].

    Google Scholar 

  59. A. Monnai and T. Hirano, Effects of bulk viscosity at freezeout, Phys. Rev. C 80 (2009) 054906 [arXiv:0903.4436] [SPIRES].

    Google Scholar 

  60. A. Monnai and T. Hirano, Effects of bulk viscosity on p T -spectra and elliptic flow parameter, Nucl. Phys. A 830 (2009) 471c [arXiv:0907.3078] [SPIRES].

    Google Scholar 

  61. S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [SPIRES].

    Article  ADS  Google Scholar 

  62. P. Romatschke, Relativistic viscous fluid dynamics and non-equilibrium entropy, Class. Quant. Grav. 27 (2010) 025006 [arXiv:0906.4787] [SPIRES].

    Article  Google Scholar 

  63. W. Israel, Nonstationary irreversible thermodynamics: a causal relativistic theory, Ann. Phys. 100 (1976) 310 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  64. W. Israel and J.M. Stewart, Transient relativistic thermodynamics and kinetic theory, Ann. Phys. 118 (1979) 341 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  65. A. Bazavov et al., Equation of state and QCD transition at finite temperature, Phys. Rev. D 80 (2009) 014504 [arXiv:0903.4379] [SPIRES].

    ADS  Google Scholar 

  66. P.B. Arnold, G.D. Moore and L.G. Yaffe, Transport coefficients in high temperature gauge theories. II: beyond leading log, JHEP 05 (2003) 051 [hep-ph/0302165] [SPIRES].

    Article  ADS  Google Scholar 

  67. H.B. Meyer, A calculation of the shear viscosity in SU(3) gluodynamics, Phys. Rev. D 76 (2007) 101701 [arXiv:0704.1801] [SPIRES].

    ADS  Google Scholar 

  68. M. Natsuume and T. Okamura, Causal hydrodynamics of gauge theory plasmas from AdS/CFT duality, Phys. Rev. D 77 (2008) 066014 [Erratum ibid. D 78 (2008) 089902] [arXiv:0712.2916] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  69. M.A. York and G.D. Moore, Second order hydrodynamic coefficients from kinetic theory, Phys. Rev. D 79 (2009) 054011 [arXiv:0811.0729] [SPIRES].

    ADS  Google Scholar 

  70. P. Huovinen and D. Molnar, The applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions, Phys. Rev. C 79 (2009) 014906 [arXiv:0808.0953] [SPIRES].

    ADS  Google Scholar 

  71. D. Molnar and P. Huovinen, Applicability of viscous hydrodynamics at RHIC, Nucl. Phys. A 830 (2009) 475c [arXiv:0907.5014] [SPIRES].

    Google Scholar 

  72. P.F. Kolb and U.W. Heinz, Hydrodynamic description of ultrarelativistic heavy-ion collisions, nucl-th/0305084 [SPIRES].

  73. B. Müller and K. Rajagopal, From entropy and jet quenching to deconfinement?, Eur. Phys. J. C 43 (2005) 15 [hep-ph/0502174] [SPIRES].

    Article  ADS  Google Scholar 

  74. J.-W. Chen and J. Wang, Bulk viscosity of a gas of massless pions, Phys. Rev. C 79 (2009) 044913 [arXiv:0711.4824] [SPIRES].

    ADS  Google Scholar 

  75. D. Fernandez-Fraile and A.G. Nicola, Bulk viscosity and the conformal anomaly in the pion gas, Phys. Rev. Lett. 102 (2009) 121601 [arXiv:0809.4663] [SPIRES].

    Article  ADS  Google Scholar 

  76. J. Noronha-Hostler, J. Noronha and C. Greiner, Transport coefficients of hadronic matter near T c , Phys. Rev. Lett. 103 (2009) 172302 [arXiv:0811.1571] [SPIRES].

    Article  Google Scholar 

  77. A. Wiranata and M. Prakash, Bulk viscosity of interacting hadrons, Nucl. Phys. A 830 (2009) 219c [arXiv:0906.5592] [SPIRES].

    Google Scholar 

  78. P.B. Arnold, C. Dogan and G.D. Moore, The bulk viscosity of high-temperature QCD, Phys. Rev. D 74 (2006) 085021 [hep-ph/0608012] [SPIRES].

    ADS  Google Scholar 

  79. G.D. Moore and O. Saremi, Bulk viscosity and spectral functions in QCD, JHEP 09 (2008) 015 [arXiv:0805.4201] [SPIRES].

    Article  ADS  Google Scholar 

  80. P. Romatschke and D.T. Son, Spectral sum rules for the quark-gluon plasma, Phys. Rev. D 80 (2009) 065021 [arXiv:0903.3946] [SPIRES].

    Google Scholar 

  81. S. Caron-Huot, Asymptotics of thermal spectral functions, Phys. Rev. D 79 (2009) 125009 [arXiv:0903.3958] [SPIRES].

    ADS  Google Scholar 

  82. H.B. Meyer, Computing the viscosity of the QGP on the lattice, Prog. Theor. Phys. Suppl. 174 (2008) 220 [arXiv:0805.4567] [SPIRES].

    Article  MATH  ADS  Google Scholar 

  83. K. Huebner, F. Karsch and C. Pica, Correlation functions of the energy-momentum tensor in SU(2) gauge theory at finite temperature, Phys. Rev. D 78 (2008) 094501 [arXiv:0808.1127] [SPIRES].

    ADS  Google Scholar 

  84. H.B. Meyer, Energy-momentum tensor correlators and spectral functions, JHEP 08 (2008) 031 [arXiv:0806.3914] [SPIRES].

    Article  Google Scholar 

  85. I. Kanitscheider and K. Skenderis, Universal hydrodynamics of non-conformal branes, JHEP 04 (2009) 062 [arXiv:0901.1487] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  86. A. Buchel, Relaxation time of non-conformal plasma, Phys. Lett. B 681 (2009) 200 [arXiv:0908.0108] [SPIRES].

    MathSciNet  Google Scholar 

  87. J.I. Kapusta, Viscous properties of strongly interacting matter at high temperature, arXiv:0809.3746 [SPIRES].

  88. G. Boyd et al., Thermodynamics of SU(3) lattice gauge theory, Nucl. Phys. B 469 (1996) 419 [hep-lat/9602007] [SPIRES].

    Article  ADS  Google Scholar 

  89. G.S. Denicol, T. Kodama, T. Koide and P. Mota, Non-linearity induced by finite size of fluid cell in causal dissipative hydrodynamics, J. Phys. G 36 (2009) 035103 [arXiv:0808.3170] [SPIRES].

    ADS  Google Scholar 

  90. S.S. Gubser, A. Nellore, S.S. Pufu and F.D. Rocha, Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics, Phys. Rev. Lett. 101 (2008) 131601 [arXiv:0804.1950] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  91. S.S. Gubser, S.S. Pufu and F.D. Rocha, Bulk viscosity of strongly coupled plasmas with holographic duals, JHEP 08 (2008) 085 [arXiv:0806.0407] [SPIRES].

    Article  ADS  Google Scholar 

  92. A. Buchel, Hydrodynamics of the cascading plasma, Nucl. Phys. B 820 (2009) 385 [arXiv:0903.3605] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  93. U. Gürsoy, E. Kiritsis, G. Michalogiorgakis and F. Nitti, Thermal transport and drag force in improved holographic QCD, JHEP 12 (2009) 056 [arXiv:0906.1890] [SPIRES].

    Article  Google Scholar 

  94. A. Buchel and C. Pagnutti, Bulk viscosity of N = 2* plasma, Nucl. Phys. B 816 (2009) 62 [arXiv:0812.3623] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  95. I. Melo et al., The Kolmogorov-Smirnov test and its use for the identification of fireball fragmentation, Phys. Rev. C 80 (2009) 024904 [arXiv:0902.1607] [SPIRES].

    ADS  Google Scholar 

  96. F. Becattini, An introduction to the statistical hadronization model, arXiv:0901.3643 [SPIRES].

  97. R. Hagedorn, Statistical thermodynamics of strong interactions at high-energies, Nuovo Cim. Suppl. 3 (1965) 147 [SPIRES].

    Google Scholar 

  98. W. Broniowski, B. Hiller, W. Florkowski and P. Bozek, Event-by-event p T fluctuations and multiparticle clusters in relativistic heavy-ion collisions, Phys. Lett. B 635 (2006) 290 [nucl-th/0510033] [SPIRES].

    ADS  Google Scholar 

  99. W. Broniowski, P. Bozek, W. Florkowski and B. Hiller, p T -fluctuations and multiparticle clusters in heavy-ion collisions, PoS(CFRNC2006)020 [nucl-th/0611069] [SPIRES].

  100. PHOBOS collaboration, B. Alver et al., System size dependence of cluster properties from two- particle angular correlations in Cu+Cu and Au+Au collisions at \( \sqrt {{s_{\text{NN}}}} = 200\;GeV \), arXiv:0812.1172 [SPIRES].

  101. U. Heinz, private communication.

  102. H. Song, Causal viscous hydrodynamics for relativistic heavy ion collisions, Ph.D. thesis, Ohio State University, Columbus U.S.A. (2009) [arXiv:0908.3656] [SPIRES].

  103. H. Song and U.W. Heinz, Interplay of shear and bulk viscosity in generating flow in heavy-ion collisions, arXiv:0909.1549 [SPIRES].

Download references

Author information

Authors and Affiliations

  1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, U.S.A.

    Krishna Rajagopal

  2. Clovis West High School, Fresno, CA, 93720, U.S.A.

    Nilesh Tripuraneni

Authors
  1. Krishna Rajagopal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nilesh Tripuraneni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Krishna Rajagopal.

Additional information

ArXiv ePrint: 0908.1785

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rajagopal, K., Tripuraneni, N. Bulk viscosity and cavitation in boost-invariant hydrodynamic expansion. J. High Energ. Phys. 2010, 18 (2010). https://doi.org/10.1007/JHEP03(2010)018

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP03(2010)018

Keywords

Search

Navigation