Universality of Quasinormal-Mode Shifts from Small Nonlocal Effective Couplings

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 $\epsilon$. Evaluation of the fractional operator in both coordinate and momentum representations reveals a universal scaling law $\delta \omega /\omega \propto \epsilon /M^{2s}$, 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.

15 pages latex, no Figure