AI 中文总结
研究引力波的引力透镜效应，通过扩展几何光学近似到高阶，结合多种方法构建方程组描述其极化沿类光测地线演化，应用于史瓦西透镜配置，揭示了透镜GW信号中表观矢量和标量模式的产生及来源。
AI 中文摘要
在这项工作中，我们通过将几何光学近似扩展到更高阶来研究引力波（GWs）的引力透镜效应。借助纽曼 - 彭罗斯形式，我们将GW传播方程重新表示为一系列标量方程，并给出描述GW极化的外尔标量的显式表达式。通过结合求解测地线偏差和输运方程的方法，我们构建了一个可解的方程组来描述GW极化沿类光测地线的演化。此框架填补了主导阶几何光学和基尔霍夫衍射积分留下的空白，它们都未捕捉到透镜过程中GW的极化特性。我们将上述框架应用于史瓦西透镜配置。通过严格的理论公式和详细的数值分析，结果揭示了透镜GW信号中出现的表观矢量和标量模式，它们源于极化平面的涂抹和波前的畸变，并非代表真正的动力学自由度，而是由引力透镜施加的传播效应产生。
英文摘要
In this work, we study the gravitational lensing of gravitational waves (GWs) by extending the geometric-optics approximation to higher order. With the help of the Newman-Penrose formalism, we reexpress the GW propagation equations as a series of scalar equations and present explicit expressions for the Weyl scalars that describe the GW polarizations. By combining the approaches of solving geodesic deviation and transport equations, we construct a solvable system of equations that describes the evolution of GW polarization along null geodesics. This framework fills the gap left by the leading-order geometric optics and the Kirchhoff diffraction integral, neither of which captures the polarization characteristics of GWs during the lensing process. This work applies the above framework to a Schwarzschild lensing configuration. Through a rigorous theoretical formulation and detailed numerical analysis, our results reveal the emergence of apparent vector and scalar modes in lensed GW signals, which originate from the smearing of the polarization plane and distortion of the wavefront and do not represent genuine dynamical degrees of freedom but rather arise as the propagation effects imposed by gravitational lensing.
Comments26 pages, 5 figures
