2025/09/29 by Pantig, Reggie C.
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2509.24479
The recent convergence of gravitational-wave (GW) observations and black hole imaging provides complementary probes of strong-gravity dynamics. While the black hole shadow is typically modeled as a static feature, a dynamically perturbed spacetime in its ringdown phase must induce temporal modulations in the shadow's apparent size and shape. We develop a theoretical framework within linear perturbation theory to investigate this shadow ringing effect for a Schwarzschild black hole. By modeling the geometry as a small, mode-selected quasinormal mode (QNM) perturbation, we treat the shadow boundary as an instantaneous separatrix of null geodesics. We derive a first-order, gauge-invariant mapping between the metric perturbation hμν and the displacement of the shadow boundary, δR(φ,t). By perturbing the effective potential for null geodesics near the unstable photon sphere (r=3M), we derive mode-resolved transfer coefficients that quantify how the QNM imprints itself onto the shadow. We predict that the shadow boundary oscillates coherently at the QNM's real frequency ω\rm Re with an exponential damping rate set by |ω\rm Im|. Furthermore, the azimuthal structure of the modulation encodes the spherical harmonic content (ℓ,m) of the driving QNM, providing a novel, geometric signature for QNM spectroscopy.