Bosonic and Fermionic love number of static acoustic black hole

TL;DR

This paper calculates static Love numbers for scalar and fermionic perturbations of acoustic black holes in various dimensions, revealing distinct behaviors and universal patterns that deepen understanding of tidal responses in analogue gravity systems.

Contribution

It introduces the first computation of Love numbers for scalar and Dirac fields in acoustic black holes, uncovering universal power-law forms and dimension-dependent behaviors.

Findings

Scalar Love number is nonzero in (3+1) dimensions.

Fermionic Love numbers follow a universal power-law form.

In (2+1) dimensions, scalar Love number vanishes for even m but not for odd m.

Abstract

We compute static ($\omega\to0$) 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 $F^{\pm1/2}_{\ell m}=\pm 4^{-(\ell+1/2)}$. 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.