Dynamical tidal response of regular black holes: Perturbative analysis and shell EFT interpretation

Abstract

We compute the frequency-dependent quadrupolar tidal response of Bardeen, Hayward, and Fan-Wang regular black holes in the polar and axial sectors by solving the coupled gravitational-electromagnetic perturbation equations numerically. Our analysis independently recovers the static Love numbers and their scaling at small regularization, while differences can occur at finite regularization due to higher-order corrections. The ratios of metric source-response coefficients at low frequencies ($ω$) have smooth corrections starting at $\mathcal{O}(ω^{2})$. Furthermore, we compare the peaks in the response coefficients with the real parts of the quasinormal mode (QNM) frequencies and find that in the polar sector for Bardeen, Hayward and Fan-Wang, peaks for small values of the regularization parameter, align with the corresponding QNM frequencies within the damping width provided by the imaginary part of the respective QNM. On the other hand, in the axial sector, the Bardeen and Hayward maxima of the response coefficients are not aligned with the real part of the QNM, whereas all the Fan-Wang peaks are. Moreover, we perform a shell EFT calculation using a scalar field as a simpler probe. The shell EFT construction expresses the response in terms of renormalised Wilson coefficients and helps isolate the scheme-dependent finite terms from the scheme-independent part. We also show that it yields the same source-response ratio as the direct calculation when the source is subtracted in the same background. This agreement, obtained in the simpler probe case, further supports the broader interpretation of the dynamical tidal response as a well-defined gauge-invariant observable.