Fermionic Love number of Reissner-Nordström black holes
Xiankai Pang, Yu Tian, Hongbao Zhang, Qingquan Jiang
TL;DR
The work addresses fermionic tidal Love numbers (TLNs) of Reissner–Nordström black holes under Weyl neutrino perturbations. It develops the Weyl equation in RN spacetime using the NP formalism in ingoing Eddington coordinates, performs variable separation with spin-weighted harmonics, and extracts TLNs from the large-distance behavior of the regular static solution. The main finding is that the fermionic TLNs are nonzero for $0\le q<1$ and purely real, vanishing only in the extremal case $q=1$, highlighting a key distinction from bosonic TLNs and a potential universality in fermionic responses. The results motivate further exploration of fermionic perturbations in black-hole spacetimes, including higher dimensions, charged fermions, and dynamical responses.
Abstract
The tidal deformation of compact objects, characterised by their Love numbers, provides insights into the internal structure of neutron stars and black holes. While bosonic tidal Love numbers vanish for black holes in general relativity, it has been recently revealed that fermionic tidal perturbations can induce non-zero Love numbers for Kerr black holes. In this paper, we investigate the response of the Reissner-Nordström black hole to the fermionic Weyl field. As a result, we find that the corresponding fermionic tidal Love numbers are also non-vanishing for the Reissner-Nordström black holes except for the extremal ones, which highlights the universal distinct behavior of the fermionic tidal Love numbers compared to the bosonic counterparts.