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arXiv · 2609.09284

Ruling out matter-induced bumps in black-hole effective potentials

Matteo Della Rocca·Romeo Felice Rosato·Paolo Pani
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Abstract

Matter fields localized around black holes can produce small secondary bumps in the effective potentials governing black-hole perturbations, potentially leading to quasinormal-mode spectral instabilities and late-time echoes. Considering physically motivated models of anisotropic fluids surrounding a spherically symmetric black hole, we show that the appearance of such a secondary bump is accompanied by either singular matter profiles or divergent characteristic speeds in the fluid. These features indicate that the corresponding matter configurations are unphysical. We further demonstrate that a secondary bump in the effective potential does not necessarily imply the existence of additional light rings in the spacetime.

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Matteo Della Rocca, Romeo Felice Rosato, Paolo Pani. 2026-09-08. Ruling out matter-induced bumps in black-hole effective potentials. https://arxiv.org/abs/2609.09284

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