First-order relativistic hydrodynamics is stable

  • Pavel KovtunEmail author
Open Access
Regular Article - Theoretical Physics


We study linearized stability in first-order relativistic viscous hydrodynamics in the most general frame. There is a region in the parameter space of transport coefficients where the perturbations of the equilibrium state are stable. This defines a class of stable frames, with the Landau-Lifshitz frame falling outside the class. The existence of stable frames suggests that viscous relativistic fluids may admit a sensible hydrodynamic description in terms of temperature, fluid velocity, and the chemical potential only, i.e. in terms of the same hydrodynamic variables as non-relativistic fluids. Alternatively, it suggests that the Israel-Stewart and similar constructions may be unnecessary for a sensible relativistic hydrodynamic theory.


Holography and quark-gluon plasmas Thermal Field Theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited


  1. [1]
    C. Eckart, The Thermodynamics of irreversible processes. III. Relativistic theory of the simple fluid, Phys. Rev. 58 (1940) 919 [INSPIRE].
  2. [2]
    S. Weinberg, Gravitation and Cosmology, John Wiley & Sons (1972) [INSPIRE].
  3. [3]
    L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Pergamon (1987).Google Scholar
  4. [4]
    W.A. Hiscock and L. Lindblom, Generic instabilities in first-order dissipative relativistic fluid theories, Phys. Rev. D 31 (1985) 725 [INSPIRE].
  5. [5]
    W.A. Hiscock and L. Lindblom, Linear plane waves in dissipative relativistic fluids, Phys. Rev. D 35 (1987) 3723 [INSPIRE].
  6. [6]
    W. Israel, Nonstationary irreversible thermodynamics: A Causal relativistic theory, Annals Phys. 100 (1976) 310 [INSPIRE].
  7. [7]
    W. Israel and J.M. Stewart, Thermodynamics of nonstationary and transient effects in a relativistic gas, Phys. Lett. A 58 (1976) 213.Google Scholar
  8. [8]
    W.A. Hiscock and L. Lindblom, Stability and causality in dissipative relativistic uids, Annals Phys. 151 (1983) 466 [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    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] [INSPIRE].
  10. [10]
    G.S. Denicol, H. Niemi, E. Molnar and D.H. Rischke, Derivation of transient relativistic uid dynamics from the Boltzmann equation, Phys. Rev. D 85 (2012) 114047 [Erratum ibid. D 91 (2015) 039902] [arXiv:1202.4551] [INSPIRE].
  11. [11]
    R.P. Geroch and L. Lindblom, Dissipative relativistic fluid theories of divergence type, Phys. Rev. D 41 (1990) 1855 [INSPIRE].
  12. [12]
    L. Rezzolla and O. Zanotti, Relativistic Hydrodynamics, Oxford (2013).Google Scholar
  13. [13]
    P. Romatschke and U. Romatschke, Relativistic Fluid Dynamics In and Out of Equilibrium, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2019) [arXiv:1712.05815] [INSPIRE].
  14. [14]
    C. Gale, S. Jeon and B. Schenke, Hydrodynamic Modeling of Heavy-Ion Collisions, Int. J. Mod. Phys. A 28 (2013) 1340011 [arXiv:1301.5893] [INSPIRE].
  15. [15]
    S. Jeon and U. Heinz, Introduction to Hydrodynamics, Int. J. Mod. Phys. E 24 (2015) 1530010 [arXiv:1503.03931] [INSPIRE].
  16. [16]
    P. Van and T.S. Biro, First order and stable relativistic dissipative hydrodynamics, Phys. Lett. B 709 (2012) 106 [arXiv:1109.0985] [INSPIRE].
  17. [17]
    H. Freistühler and B. Temple, Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation, Proc. Roy. Soc. Lond. A 470 (2014) 0055.Google Scholar
  18. [18]
    H. Freistühler and B. Temple, Causal dissipation for the relativistic dynamics of ideal gases, Proc. Roy. Soc. Lond. A 473 (2017) 0729.Google Scholar
  19. [19]
    F.S. Bemfica, M.M. Disconzi and J. Noronha, Causality and existence of solutions of relativistic viscous uid dynamics with gravity, Phys. Rev. D 98 (2018) 104064 [arXiv:1708.06255] [INSPIRE].
  20. [20]
    S. Bhattacharyya, Constraints on the second order transport coefficients of an uncharged fluid, JHEP 07 (2012) 104 [arXiv:1201.4654] [INSPIRE].
  21. [21]
    S. Bhattacharyya, Entropy current and equilibrium partition function in fluid dynamics, JHEP 08 (2014) 165 [arXiv:1312.0220] [INSPIRE].
  22. [22]
    P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].
  23. [23]
    J. Hernandez and P. Kovtun, Relativistic magnetohydrodynamics, JHEP 05 (2017) 001 [arXiv:1703.08757] [INSPIRE].
  24. [24]
    S. Bhattacharyya, Entropy Current from Partition Function: One Example, JHEP 07 (2014) 139 [arXiv:1403.7639] [INSPIRE].
  25. [25]
    N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Jain, S. Minwalla and T. Sharma, Constraints on Fluid Dynamics from Equilibrium Partition Functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].
  26. [26]
    K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].
  27. [27]
    L.D. Landau and E.M. Lifshitz, Statistical Physics, Part I, Pergamon (1980).Google Scholar
  28. [28]
    E. Krotscheck and W. Kundt, Causality criteria, Commun. Math. Phys. 60 (1978) 171.Google Scholar
  29. [29]
    P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].
  30. [30]
    G. Festuccia and H. Liu, A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes, Adv. Sci. Lett. 2 (2009) 221 [arXiv:0811.1033] [INSPIRE].
  31. [31]
    J.F. Fuini, C.F. Uhlemann and L.G. Yaffe, Damping of hard excitations in strongly coupled \( \mathcal{N} \) = 4 plasma, JHEP 12 (2016) 042 [arXiv:1610.03491] [INSPIRE].
  32. [32]
    J. Bhattacharya, S. Bhattacharyya, S. Minwalla and A. Yarom, A Theory of first order dissipative superuid dynamics, JHEP 05 (2014) 147 [arXiv:1105.3733] [INSPIRE].
  33. [33]
    R. Loganayagam, Entropy Current in Conformal Hydrodynamics, JHEP 05 (2008) 087 [arXiv:0801.3701] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics & AstronomyUniversity of VictoriaVictoriaCanada

Personalised recommendations