Fermionic Love number of higher-dimensional Reissner-Nordström black holes

Abstract

In this paper, we generalize our previous work on the fermionic tidal Love numbers (TLNs) to higher-dimensional Reissner-Nordström black holes. The massless Dirac equation is solved in $D$-dimensional spacetime using ingoing Eddington coordinates and regular tetrads. After identifying the regular solution branch, we extract the fermionic TLNs from its asymptotic behavior at infinity. The resulting TLNs exhibit a rich dimension-dependent structure that generalizes the four-dimensional case. Unlike bosonic TLNs, which vanish for certain values of the total angular momentum $l$ in dimensions $D>4$, fermionic TLNs remain non-zero for all $l$ and $D\ge 4$, except for extremal black holes. Moreover, the $l$-dependence weakens as $D$ increases, disappearing entirely in the infinite-dimensional limit. These results provide new insights into black hole responses to fermionic perturbations in higher-dimensional spacetimes.

15 pages; comments welcome