- Open Access
- Access by Xinjiang University
Relativistic transport near moving interfaces
Phys. Rev. D 114, 104005 – Published 3 November, 2026
DOI: https://doi.org/10.1103/6ldz-p4s1
Abstract
We study linear disturbances localized near planar surfaces moving at constant velocity in relativistic media. Depending on the physical setting, the surface may represent a moving obstacle, a thermal boundary, or an external source, providing a unified description of boundary layers, wakes, and the asymptotic tails of shock waves. The central result is a propagator representation of the interface solution that yields a geometric characterization of these phenomena. Using a Laplace-transform formulation, we show that the solution is a superposition of modes with purely imaginary frequency and wave number. For a given interface velocity, the admissible modes are selected by the line in the plane. As varies, this line sweeps across the spectrum, providing a unified geometric description of interface-localized solutions for arbitrary interface velocities. We illustrate the formalism with applications to relativistic hydrodynamics and kinetic theory.
Physics Subject Headings (PhySH)
Article Text
References (28)
- K. Case, Ann. Phys. (N.Y.) 9, 1 (1960).
- Y. B. Zel’dovich and Y. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, edited by W. D. Hayes and R. F. Probstein (Academic Press, New York, 1967).
- D. Mihalas and B. Weibel Mihalas, Foundations of Radiation Hydrodynamics (Oxford University Press, New York, 1984).
- A. K. Prinja and E. W. Larsen, General principles of neutron transport, in Handbook of Nuclear Engineering, edited by D. G. Cacuci (Springer US, Boston, MA, 2010), pp. 427–542.
- H. Schlichting and K. Gersten, Boundary-Layer Theory, 9th ed. (Springer, Berlin, Heidelberg, 2017).
- I. Novak, J. Sonner, and B. Withers, Phys. Rev. D 98, 086023 (2018).
- E. I. Kiselev and J. Schmalian, Phys. Rev. B 99, 035430 (2019).
- L. Gavassino, arXiv:2607.10148.
- L. Gavassino, M. M. Disconzi, and J. Noronha, Phys. Rev. Lett. 132, 222302 (2024).
- L. Gavassino, Phys. Rev. D 110, 094012 (2024).
- L. Gavassino, Phys. Rev. Lett. 137, 022301 (2026).
- T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Grundlehren der mathematischen Wissenschaften Vol. 132 (Springer-Verlag, Berlin, Heidelberg, New York, 1980), corrected printing of the second edition.
- C. Cattaneo, Sur une forme de l’équation de la chaleur éliminant le paradoxe d’une propagation instantanée, Comptes rendus hebdomadaires des séances de l’Académie des sciences (Gauthier-Villars, Paris, 1958).
- D. Jou, J. Casas-Vázquez, and G. Lebon, Rep. Prog. Phys. 51, 1105 (1999).
- L. Gavassino, M. Antonelli, and B. Haskell, Phys. Rev. D 106, 056010 (2022).
- W. A. Hiscock and L. Lindblom, Ann. Phys. (N.Y.) 151, 466 (1983).
- L. Rezzolla and O. Zanotti, Relativistic Hydrodynamics (Oxford University Press, Oxford, 2013).
- L. Gavassino, M. Antonelli, and B. Haskell, Phys. Rev. Lett. 128, 010606 (2022).
- W. Israel and J. Stewart, Ann. Phys. (N.Y.) 118, 341 (1979).
- S. Pu, T. Koide, and D. H. Rischke, Phys. Rev. D 81, 114039 (2010).
- N. Mullins, M. Hippert, and J. Noronha, Phys. Rev. D 108, 076013 (2023).
- T. S. Olson and W. A. Hiscock, Ann. Phys. (N.Y.) 204, 331 (1990).
- F. S. Bemfica, Phys. Rev. E 112, 065105 (2025).
- J. L. Anderson and H. R. Witting, Physica (Amsterdam) 74, 466 (1974).
- C. Cercignani and G. M. Kremer, The Relativistic Boltzmann Equation: Theory and Applications (Birkhäuser, Basel, 2002).
- F. Becattini, Acta Phys. Pol. B 47, 1819 (2016).
- L. Gavassino, Found. Phys. 50, 1554 (2020).
- T. S. Olson, Ann. Phys. (N.Y.) 199, 18 (1990).
