Tidal Love numbers and the dynamical instability of AdS bubbles

In this work, we study non-radial perturbations of AdS bubbles and their tidal Love numbers (TLNs). The odd- and even-parity TLNs are computed up to $l=6$ in the limit $k\to \mathrm{\infty }$. The odd-parity TLNs are found to be negative, while the even-parity TLNs are positive for ${\upsilon }_s^2=-1$. As $l$ increases, the tidal Love numbers approach zero. The TLNs of the even-parity sector up to order $l=41$ are also calculated over the entire parameter space of $k$, from $0$ to $\mathrm{\infty }$. We find that in the region where $p\mathrm{/}\sigma >0$, an increasing number of TLNs become negative as $l$ increases. For $l=41$, the highest order we have examined, the TLNs are negative everywhere except in a narrow region very close to the zero of $p\mathrm{/}\sigma$, which agrees well with the instability criterion in the eikonal limit for self-gravitating membranes proposed by Yang {\it et al.}\ [P. R. L. {\bf 130}, 011402 (2023)].