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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2509.24479 |
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| _version_ | 1866908857874251776 |
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| author | Pantig, Reggie C. |
| author_facet | Pantig, Reggie C. |
| contents | 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 $h_{μν}$ 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 $(\ell,m)$ of the driving QNM, providing a novel, geometric signature for QNM spectroscopy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shadow Ringing of Black Holes from Photon Sphere Quasinormal Modes Pantig, Reggie C. High Energy Physics - Theory 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 $h_{μν}$ 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 $(\ell,m)$ of the driving QNM, providing a novel, geometric signature for QNM spectroscopy. |
| title | Shadow Ringing of Black Holes from Photon Sphere Quasinormal Modes |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.24479 |