Tidal Love numbers for regular black holes

TL;DR

The paper addresses whether regular black holes (RBHs) exhibit nonzero tidal Love numbers (TLNs) and how their interiors influence tidal responses. It develops a unified analytic Green’s-function framework to compute TLNs for three RBH models—Bardeen, sub-Planckian-curvature, and ASG—under scalar, vector, and axial gravitational perturbations. The main finding is that TLNs are generically nonzero and exhibit strong model- and mode-dependence, with higher-order corrections often containing logarithmic terms that resemble renormalization-group running, signaling scale-dependent tidal responses. These results imply that TLNs can imprint observable fingerprints of RBH interiors in gravitational waves, offering a pathway to test quantum-gravity-inspired BH models with future detectors.

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 new 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 establish TLNs as promising probes for testing regular black hole models with future gravitational-wave observations.