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  • Letter
  • Open Access

Fermionic response of black holes in general relativity

Sumanta Chakraborty1,*, Pierre Heidmann2,†, and Paolo Pani3,‡

  • *Contact author: tpsc@iacs.res.in
  • †Contact author: heidmann.5@osu.edu
  • ‡Contact author: paolo.pani@uniroma1.it
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Phys. Rev. D 113, L061503 – Published 16 March, 2026

DOI: https://doi.org/10.1103/2yr1-9ymw

Abstract

Black holes in general relativity exhibit a remarkable feature: their response to static scalar, electromagnetic, and gravitational perturbations—as quantified by the so-called tidal Love numbers—vanishes identically. We present the first exception to this rule: the Love numbers of a black hole perturbed by a fermionic field are nonzero. We derive a closed-form expression of these fermionic Love numbers for generic spin in the background of a Kerr black hole with arbitrary angular momentum. In contrast, we show that the fermionic dissipation numbers vanish for static perturbations, reflecting the absence of superradiance for fermions. These results highlight a fundamental distinction between bosonic and fermionic perturbations, which can be interpreted as a breaking of the hidden symmetries that underlie the vanishing of Love numbers in the bosonic sector.

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Phys. Rev. D 113, L061503– Published 16 March, 2026
  • Received 3 September 2025
  • Accepted 19 February 2026
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