Universality of Quasinormal-Mode Shifts from Small Nonlocal Effective Couplings

Anisur Rahaman

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arXiv · 2511.11726

Universality of Quasinormal-Mode Shifts from Small Nonlocal Effective Couplings

Anisur Rahaman

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Abstract

We investigate perturbative quasinormal-mode (QNM) shifts of black holes arising from fractional, nonlocal modifications to the wave operator. Starting from a scalar master equation corrected by a small fractional Laplacian term $(-\Delta)^{s}$ with $0<s<1$, we derive an analytic expression for the complex frequency shift at first order in the nonlocal coupling $\varepsilon$. Evaluation of the fractional operator in both coordinate and momentum representations reveals a universal scaling law $\delta\omega/\omega \propto \varepsilon/M^{2s}$, largely independent of the field spin, with an additional $\ell^{2s}$ enhancement in the eikonal regime $\ell \gg 1$. Applying the formalism to Schwarzschild, slowly rotating Kerr, Hayward regular, and LQG-corrected black holes, we demonstrate that the leading-order fractional QNM shift is universal, with geometric details entering only through overlap integrals of the mode functions. This universality provides a model-independent signature of nonlocality in strong-gravity ringdown spectra and offers a potential observational window into quantum-gravity-inspired modifications.

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Anisur Rahaman. 2025-11-13. Universality of Quasinormal-Mode Shifts from Small Nonlocal Effective Couplings. https://arxiv.org/abs/2511.11726

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