# Fermionic Love of Black Holes in General Relativity

## TL;DR

This paper discovers that Kerr black holes respond differently to fermionic perturbations by having nonzero Love numbers, unlike the zero Love numbers for bosonic fields, revealing a fundamental symmetry difference.

## Contribution

It provides the first explicit calculation of nonzero fermionic Love numbers for Kerr black holes, highlighting a key difference from bosonic perturbations.

## Key findings

- Fermionic Love numbers are nonzero for Kerr black holes.
- Fermionic dissipation numbers vanish for static perturbations.
- The results indicate a symmetry breaking between bosonic and fermionic perturbations.

## 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.