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arXiv · 2608.01061

Optimal frequency scales for probing black-hole geometries

Saulo Albuquerque·Sebastian H. Völkel
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Abstract

Can gravitational waves probe the near-horizon geometry of black holes, and if yes, which frequency scale is optimal? Although shorter wavelengths usually resolve smaller scales, we show that black-hole scattering may impose an information-theoretic optimum. We study a controlled scattering Gedankenexperiment in which Gaussian pulses of scalar test fields are sent toward a black- hole potential and the reflected waveform is used to infer the geometry. Near-horizon deviations are parametrized with the Rezzolla-Zhidenko metric, and information recovery is quantified by the Fisher matrix in the high-signal-to-noise limit. Narrow, high-frequency pulses resolve short scales but are mostly transmitted through the barrier, while wide pulses are efficiently reflected but poorly resolve the potential. Their competition selects an optimal pulse width, numerically found to be set by about the inverse square root of the potential peak. Using the P\"oschl-Teller analytical solutions, we further model the correct excitation of quasinormal modes and separate the information in the fundamental mode from that in the full waveform, including the prompt response. The optimal probe is therefore not the highest-frequency pulse, but the waveform that balances spatial resolution against reflected information, linking black-hole spectroscopy, semiclassical barrier scattering, and information theory.

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Saulo Albuquerque, Sebastian H. Völkel. 2026-08-02. Optimal frequency scales for probing black-hole geometries. https://arxiv.org/abs/2608.01061

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