In general relativity, the tidal Love numbers for static scalar, electromagnetic, and gravitational perturbations of black holes are zero. For the first time, an exception is presented: fermionic Love numbers are non-zero. A closed analytical expression is obtained for these numbers in the Kerr spacetime with arbitrary angular momentum and for general spin of the fermionic field. It is shown that in the static limit, the fermionic dissipative numbers vanish, consistent with the absence of superradiance for fermions. The results reveal a fundamental difference between bosonic and fermionic perturbations, which can be interpreted as a violation of the hidden symmetries underlying the vanishing of Love numbers in the bosonic sector.
Black holes are regions of such intense spacetime curvature that not even light can escape. For a long time, they were thought to be utterly unyielding: neither light waves nor gravitational disturbances leave a dent on them. They're like the still surface of a dark lake, remaining unmoved no matter how long you shine a flashlight on it. But new research has shown: fields made of matter particles, such as electrons or neutrinos, make the black hole bend — just like a thrown stone sends ripples across the water. This is the first time an external influence breaks the rigidity of a black hole, and it points to a profound difference between force-carrier fields and particle fields. For non-rotating holes, these "stone" deformations don't fade: energy doesn't flow into the hole, it merely leaves an imprint. This contradicts the hidden symmetries that previously explained why black holes were impervious to ordinary fields. Fermions see gravity differently — and render it vulnerable.
🎯 The name 'Love numbers' comes from the mathematician's surname, not the English word love — it has nothing to do with feelings.