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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2510.19849 |
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| _version_ | 1866912898404581376 |
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| author | Pantig, Reggie C. |
| author_facet | Pantig, Reggie C. |
| contents | Is it possible to find imprints of a black hole ringdown through gravitational lensing? To address this question, we formulate an analytic description of weak-field and strong-deflection lensing of light in a time-dependent, perturbed Schwarzschild spacetime. The spacetime dynamics are modeled by a single, axisymmetric, even-parity quasinormal mode with \(\ell=2\), \(m=0\) and complex frequency \(ω\). Working to first order in a small perturbation amplitude while keeping background null geodesics exact, we derive a time-dependent line-of-sight (Born) expression for the screen-plane deflection measured by a static observer at large radius. From the same integral, an asymptotic expansion yields the familiar weak-field \(1/b\) law with a ringdown-frequency correction that drives a harmonic centroid wobble, whereas a near-photon-sphere expansion produces a time-dependent generalization of the logarithmic strong-deflection limit with modulated coefficients, including a small oscillation of the critical impact parameter. An observer tetrad built from the background static frame ensures that all screen-plane quantities, such as centroid motion, multi-image hierarchy, and time delays, as well as photon-ring morphology, are gauge-safe at first order. We provide explicit matching across regimes, showing that the near-critical coefficients governing spacing and ring-radius modulations are encoded in the same Born kernel that controls the weak-field correction. This provides an analytic account of how ringdown-scale perturbations enter imaging observables, without resorting to numerical integration of null geodesics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-Dependent Black Hole Lensing from Ringdown Quasinormal Mode Pantig, Reggie C. High Energy Physics - Theory General Relativity and Quantum Cosmology Is it possible to find imprints of a black hole ringdown through gravitational lensing? To address this question, we formulate an analytic description of weak-field and strong-deflection lensing of light in a time-dependent, perturbed Schwarzschild spacetime. The spacetime dynamics are modeled by a single, axisymmetric, even-parity quasinormal mode with \(\ell=2\), \(m=0\) and complex frequency \(ω\). Working to first order in a small perturbation amplitude while keeping background null geodesics exact, we derive a time-dependent line-of-sight (Born) expression for the screen-plane deflection measured by a static observer at large radius. From the same integral, an asymptotic expansion yields the familiar weak-field \(1/b\) law with a ringdown-frequency correction that drives a harmonic centroid wobble, whereas a near-photon-sphere expansion produces a time-dependent generalization of the logarithmic strong-deflection limit with modulated coefficients, including a small oscillation of the critical impact parameter. An observer tetrad built from the background static frame ensures that all screen-plane quantities, such as centroid motion, multi-image hierarchy, and time delays, as well as photon-ring morphology, are gauge-safe at first order. We provide explicit matching across regimes, showing that the near-critical coefficients governing spacing and ring-radius modulations are encoded in the same Born kernel that controls the weak-field correction. This provides an analytic account of how ringdown-scale perturbations enter imaging observables, without resorting to numerical integration of null geodesics. |
| title | Time-Dependent Black Hole Lensing from Ringdown Quasinormal Mode |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2510.19849 |