Dissipative relativistic fluid dynamics is not always causal and can favor super-luminal signal propagation under certain circumstances. On the other hand, high-energy nuclear collisions have a microscopic description in terms of QCD and are expected to follow the causality principle of special relativity. We discuss under which conditions the fluid evolution equations for a radial expansion are hyperbolic and that terms of second order in the Knudsen number are problematic for causality. We also outline briefly how this can be remedied with terms of higher order in a formal derivative expansion. The expansion dynamics are causal in the relativistic sense if the characteristic velocities are smaller than the speed of light. We obtain a concrete inequality from this constraint and discuss how it can be violated for certain initial conditions. Finally we argue that causality poses a bound on the applicability of relativistic fluid dynamics.
I. Muller, Zum Paradoxon der Warmeleitungstheorie (in German), Z. Phys. 198 (1967) 329 [INSPIRE].
W. Israel and J.M. Stewart, Transient relativistic thermodynamics and kinetic theory, Annals Phys. 118 (1979) 341 [INSPIRE].
G.S. Denicol, H. Niemi, E. Molnar and D.H. Rischke, Derivation of transient relativistic fluid dynamics from the Boltzmann equation, Phys. Rev. D 85 (2012) 114047 [Erratum ibid. D 91 (2015)039902] [arXiv:1202.4551] [INSPIRE].
P. Kostadt and M. Liu, Causality and stability of the relativistic diffusion equation, Phys. Rev. D 62 (2000) 023003 [INSPIRE].
P. Kostadt and M. Liu, Alleged acausality of the diffusion equations: a reply, Phys. Rev. D 64 (2001) 088504 [INSPIRE].
W.A. Hiscock and L. Lindblom, Stability and causality in dissipative relativistic fluids, Annals Phys. 151 (1983) 466 [INSPIRE].
R.P. Geroch and L. Lindblom, Dissipative relativistic fluid theories of divergence type, Phys. Rev. D 41 (1990) 1855 [INSPIRE].
R. Penrose, Conformal treatment of infinity, in Relativité, Groupes et Topologie: proceedings, Ecole d’été de Physique Théorique, Session XIII, Les Houches, France, 1 July-24 August 1963 [Gen. Rel. Grav. 43 (2011) 901] [INSPIRE].
R. Courant and D. Hilbert, Methods of mathematical physics, volume II, Interscience Publishers, New York, U.S.A., (1962).
L. Rezzolla and O. Zanotti, Relativistic hydrodynamics, Oxford University Press, Oxford, U.K., (2013) [ISBN-10:0198528906] [ISBN-13:978-0198528906].
A. Buchel, M.P. Heller and J. Noronha, Entropy production, hydrodynamics and resurgence in the primordial quark-gluon plasma from holography, Phys. Rev. D 94 (2016) 106011 [arXiv:1603.05344] [INSPIRE].
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.
ArXiv ePrint: 1711.06687
About this article
Cite this article
Floerchinger, S., Grossi, E. Causality of fluid dynamics for high-energy nuclear collisions. J. High Energ. Phys. 2018, 186 (2018). https://doi.org/10.1007/JHEP08(2018)186