Tidal Love numbers for regular black holes (2512.05767v1)

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.