Dynamical Tidal Response of Regular Black Holes: Perturbative Analysis and Shell EFT Interpretation

TL;DR

This paper analyzes the frequency-dependent tidal response of regular black holes, revealing complex dispersion and resonance features, and introduces an effective field theory framework to interpret these responses as meaningful observables.

Contribution

It provides the first detailed perturbative and EFT analysis of dynamical tidal Love numbers for regular black holes, including their frequency dependence and renormalization structure.

Findings

Frequency-dependent Love numbers exhibit strong dispersion and resonances.

The response smoothly approaches static limits at zero frequency.

Shell EFT offers a gauge-invariant description and clarifies renormalization of tidal responses.

Abstract

We investigate the frequency-dependent (dynamical) tidal response of regular black holes for the Bardeen, Hayward, and Fan-Wang geometries. Our results are obtained by solving the coupled perturbation equations with appropriate boundary conditions, together with a `shell effective field theory' (EFT) construction in which the tidal response is encoded in renormalized, frequency-dependent response functions. In the polar sector, the frequency-dependent Love numbers exhibit strong dispersion, including oscillatory and resonant features, while smoothly recovering the static results in the zero-frequency limit. In the axial sector, where gravitational and electromagnetic perturbations remain coupled, the response shows a simpler but strongly frequency-dependent enhancement near extremality. The shell EFT analysis provides a gauge-invariant effective description of the tidal response and clarifies its renormalization structure, including the separation of scheme-independent logarithmic running and scheme-dependent finite contributions to the response coefficients, with the corresponding Wilson coefficients determined by matching to the black hole perturbation theory. Our results establish dynamical tidal Love numbers as well-defined EFT observables for regular black holes and show that they encode information about near-horizon and interior structure that is not accessible in the static limit.