Bosonic and Fermionic love number of static acoustic black hole

Yongbin Du; Xiangdong Zhang

doi:10.1103/35lw-pvfz

paper

Bosonic and Fermionic love number of static acoustic black hole

arXiv:2512.23305 · doi:10.1103/35lw-pvfz

Abstract

We compute static ( $ω \to 0$ ) tilde Love numbers for scalar ( $s = 0$ ) and Dirac ( $s = 1/2$ ) perturbations of static acoustic black holes (ABHs) in (3+1) and (2+1) dimensions respectively. By imposing horizon regularity condition and matching to the large-radius expansion, we extract the ratio between decaying and growing modes. It turns out that in (3+1) dimensions the scalar Love number is generically nonzero for ABHs, while the Fermionic Love numbers follow a universal power-law form $F_{ℓ m}^{\pm 1/2} = \pm 4^{- (ℓ + 1/2)}$ . In (2+1) dimensions the scalar field exhibits a strange logarithmic structure, causing the Bosonic Love number to vanish for even $m$ but remain nontrivial for odd $m$ ; In contrast, the Fermionic Love number in this case retains a simple power-law form $F_{m} = 4^{- m}$ and is generically nonzero. These results provide insights into tidal response in analogue gravity systems and highlight qualitative differences between integer- and half-integer-spin fields.

12 pages

Bosonic and Fermionic love number of static acoustic black hole

Abstract

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