The work develops a covariant perturbative formalism for polarized photon propagation in arbitrary curved spacetimes. A compact expression for the polarization angle (PA) swing during the ringdown phase of a Kerr black hole is derived, explicitly revealing temporal synchronization with quasinormal modes. The result is confirmed by dynamical ray-tracing computations across a wide range of photon trajectories. Photons passing through the strong-field region exhibit achromatic damped PA oscillations with amplitudes up to ~10°, the phase set by the angular structure of the mode. This effect imprints distinctive signatures in spatially resolved autocorrelations and opens a novel polarimetric window for observing black hole mergers and their ringdown.
The merger of black holes produces powerful gravitational waves, whose final stage — the ringdown — carries key information about the mass, spin, and charge of the resulting black hole, in accordance with the 'no-hair' theorems. Existing detectors like LIGO/Virgo pick up this ringdown, but their sensitivity is insufficient for detailed spectroscopy. An alternative approach is to use polarimetry of electromagnetic radiation from the black hole’s vicinity: accretion disks, jets from active galactic nuclei, or lensed background blazars. As early as the works of John Wheeler, it was emphasized that spacetime geometry can alter light’s polarization, but direct observation of this effect from gravitational waves has only now become possible.
The authors constructed a covariant first-order perturbation theory for polarized light propagation in dynamic spacetime. In the geometric optics limit, polarization is parallel-transported along null geodesics, and the gravitational influence reduces to a local angular velocity of polarization rotation, generalizing the plane-wave result. For specific calculations, the Kerr metric with a linearized gravitational-wave perturbation was used, described by the Teukolsky equations and the CCK formalism. Numerical simulations via backward ray tracing allowed the evolution of the polarization angle to be tracked for a broad class of trajectories — from sources in the equatorial plane (modeling an accretion disk) and from infinity (modeling background objects).
It was found that for photons emitted from an accretion disk or a jet (as observed in blazars), the time dependence of the polarization angle rotation ϑ(t) follows a damped harmonic: ϑ ∝ e^{-ω_I t} cos(ω_R t - Φ), where ω_R and ω_I are the real and imaginary parts of the quasinormal mode frequency. For the fundamental mode (l=m=2) of a rotating black hole with a=0.7M, the rotation amplitude reaches ~10° when the photon passes close to the horizon (b≈4M). The phase Φ is directly linked to the azimuthal number m: Φ = m φ + const, as demonstrated in images with different φ. For photons from distant sources at late times, the signal transitions to a power-law tail ∝ t^{-3}, arising from the alignment of the photon’s wave vector with the direction of the gravitational wave. Correlation analysis of the two-point autocorrelation function confirms the signal’s robustness to noise and allows extraction of the frequency and damping rate even at a signal-to-noise ratio ~0.
This work opens a new polarimetric window into gravitational-wave astronomy. The polarization ringdown is achromatic, which helps separate it from plasma Faraday rotation, and has a predictable temporal structure. It can serve as an independent test of general relativity in strong fields, complementing measurements of gravitational waves by ground-based and space interferometers.
In the future, the method could be extended to superpositions of higher overtones, enabling extraction of more parameters from the ringdown. Joint numerical simulations that include magnetohydrodynamics of accretion flows and realistic plasma will help assess the contribution of astrophysical noise. Observations with next-generation telescopes (EHT, ngVLA, space-based polarimeters) coordinated with gravitational-wave detectors (LISA, Einstein Telescope) will test predictions on actual merger events of supermassive black holes at the centers of active galaxies.
The results will impact black hole astrophysics, gravitational-wave astronomy, high-resolution polarimetry, and tests of modified theories of gravity, where the quasinormal mode spectrum may differ.
Next steps include detailed modeling of polarization responses from accretion flows with magnetic fields and turbulence, and developing algorithms to extract the ringdown signal from the source’s intrinsic variability.
This work directly addresses the problem of testing the no-hair theorems for black holes and understanding strong-field dynamics, where classical GR tests are limited to weak-field observations.
🎯 Unlike Faraday rotation in plasma, which strongly depends on wavelength, the gravitationally induced polarization rotation is the same for all frequencies — an achromatic 'gravitational Faraday effect' predicted back in the 1950s, but only now quantitatively evaluated for realistic scenarios.