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 $v$ 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 $iÏ=vik$ in the $\{iÏ,ik\}$ plane. As $v$ 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!