AI 中文总结
该研究针对相对论介质中运动界面附近的线性扰动，通过传播子表示结合拉普拉斯变换，为边界层等界面局域化解提供统一几何描述，并在相对论流体动力学和动理学理论中进行了应用说明。
AI 中文摘要
我们研究相对论介质中以恒定速度$v$运动的平面表面附近的线性扰动。根据物理场景，该表面可代表运动障碍物、热边界或外部源，为边界层、尾流和激波的渐近尾提供统一描述。核心结果是界面解的传播子表示，该表示对这些现象给出几何刻画。利用拉普拉斯变换形式，我们证明解是纯虚频率和波数的模式叠加。对于给定的界面速度，可允许模式由$\text{\textbraceleft}i\ ext{\textomega},ik\text{\textbraceright}$平面中的直线$i\text{\textomega}=vik$选取。当$v$变化时，该直线扫过整个谱，为任意界面速度下的界面局域化解提供统一几何描述。我们将该形式主义应用于相对论流体动力学和动理学理论以作说明。
英文摘要
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 $iω=vik$ in the $\{iω,ik\}$ 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.
Comments20 pages, 7 figure, comments welcome!
