Fermionic Love of Black Holes in General Relativity

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.

Figures (1)

• Figure 1: Fermionic Love number of a Kerr black hole to massless spin $s=1/2$ perturbations as a function of the black-hole dimensionless angular momentum for some values of $(\ell,m)$. Note that $\mathcal{F}_{\pm\frac{1}{2}\ell m}$ is finite in the extremal ($a\to M$) limit and depends on $m$ only through $m^2$.