Tidal Love numbers for regular black holes

TL;DR

This paper analytically studies the tidal Love numbers of various regular black holes, revealing they are generally nonzero and highly dependent on the model and perturbation mode, with potential observational implications.

Contribution

It provides a unified analytic framework for calculating TLNs of regular black holes, highlighting their nonvanishing and model-dependent nature, unlike classical black holes.

Findings

TLNs of regular black holes are generally nonzero.

TLNs exhibit strong dependence on black hole models and perturbation modes.

Higher-order corrections show logarithmic scale dependence, similar to quantum field theory.

Abstract

Tidal Love numbers (TLNs) characterize the response of compact objects to external tidal fields and vanish for classical Schwarzschild and Kerr black holes in general relativity. Nonvanishing TLNs therefore provide a potential observational window into beyond-classical physics. In this work, we present a unified and fully analytic study of the TLNs of three representative classes of regular black holes -- the Bardeen black hole, the black hole with sub-Planckian curvature, and the black hole arising in asymptotically safe gravity -- under scalar, vector, and axial gravitational perturbations. Employing a Green's function method combined with systematic perturbative expansions, we show that TLNs of regular black holes are generically nonzero and exhibit strong model and mode dependence. In many cases, higher-order corrections develop logarithmic scale dependence, closely resembling renormalization-group running in quantum field theory and revealing a scale-dependent tidal response absent in classical black holes. Our analysis demonstrates that the internal structure of regular black holes, including de Sitter or Minkowski cores and quantum-gravity-inspired modifications, leaves distinct fingerprints in their tidal properties. These results provide a comparative theoretical benchmark for assessing regular black-hole models and establish a basis for future phenomenological and observational studies with gravitational-wave detectors.