Relativistic transport near moving interfaces
arXiv:2607.28569
The paper studies linear disturbances near planar surfaces moving at constant speed in relativistic media, presenting a propagator-based geometric framework that unifies the description of boundary layers, wakes, and shock-wave tails, with examples from relativistic hydrodynamics and kinetic theory.
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 wavenumber. 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.
20 pages, 7 figure, comments welcome!