- Open Access
Stationary Couette-type flows in relativistic fluids
Phys. Rev. D 113, 054011 – Published 6 March, 2026
DOI: https://doi.org/10.1103/crvh-vwh8
Abstract
We investigate a class of stationary, planar-symmetric solutions of relativistic hydrodynamics, in which a dissipative fluid is confined between two parallel plates that move relative to each other and/or are maintained at different temperatures. We find that neglecting the heat flux leads to qualitatively incorrect flow profiles, even in systems with temperature-independent viscosity. This arises from the fact that, in special relativity, the heat flux itself contributes to the momentum density (the so-called “inertia of heat”). This effect is most evident in the Landau frame, where the fluid removes the excess energy generated by viscous heating by streaming across the boundaries. The analysis is further extended to the limit of vanishing chemical potential.
Physics Subject Headings (PhySH)
Article Text
References (23)
- H. Schlichting and K. Gersten, Boundary-Layer Theory, 9th ed. (Springer-Verlag, Berlin, Heidelberg, 2017), pp. xxviii + 805.
- A. D. Rogava, arXiv:plasm-ph/9604003.
- C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W.H. Freeman and Co., San Francisco, 1973).
- A. Granik and G. Chapline, Phys. Fluids 8, 269 (1996).
- C. Eckart, Phys. Rev. 58, 919 (1940).
- L. Landau and E. Lifshitz, Fluid Mechanics (Elsevier Science, New York, 2013), Vol. 6.
- T. S. Olson, Ann. Phys. (N.Y.) 199, 18 (1990).
- W. Hiscock and L. Lindblom, Phys. Rev. D 31, 725 (1985).
- P. Kostädt and M. Liu, Phys. Rev. D 62, 023003 (2000).
- L. Gavassino, Phys. Rev. X 12, 041001 (2022).
- W. Israel and J. Stewart, Ann. Phys. (N.Y.) 118, 341 (1979).
- L. Gavassino, M. Antonelli, and B. Haskell, Phys. Rev. D 106, 056010 (2022).
- G. S. Denicol, H. Niemi, E. Molnár, and D. H. Rischke, Phys. Rev. D 85, 114047 (2012).
- G. S. Denicol, T. Koide, and D. H. Rischke, Phys. Rev. Lett. 105, 162501 (2010).
- G. S. Denicol, S. Jeon, and C. Gale, Phys. Rev. C 90, 024912 (2014).
- K. Huang, Statistical Mechanics, 2nd ed. (John Wiley & Sons, New York, 1987).
- L. Rezzolla and O. Zanotti, Relativistic Hydrodynamics, edited by L. Rezzolla and O. Zanotti (Oxford University Press, New York, 2013), [Amazon][WorldCat]; [Amazon][WorldCat].
- S. Weinberg, Astrophys. J. 168, 175 (1971).
- L. Gavassino, M. Antonelli, and B. Haskell, Classical Quantum Gravity 38, 075001 (2021).
- P. Kovtun, J. High Energy Phys. 10 (2019) 034.
- L. Gavassino, M. M. Disconzi, and J. Noronha, Phys. Rev. Lett. 132, 222302 (2024).
- N. Udey and W. Israel, Mon. Not. R. Astron. Soc. 199, 1137 (1982).
- L. Gavassino, Astrophys. Space Sci. 370, 4 (2025).
