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  • Open Access

Tidal Love numbers for regular black holes

Rui Wang, Qi-Long Shi, Wei Xiong, and Peng-Cheng Li*

  • *Contact author: pchli2021@scut.edu.cn
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APS Open Sci. 1, 000010 – Published 29 April, 2026

DOI: https://doi.org/10.1103/v16l-ns9s

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.

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APS Open Sci. 1, 000010– Published 29 April, 2026
Vol. 1
  • Received 9 December 2025
  • Accepted 1 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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