Hidden symmetries for tidal Love numbers: Generalities and applications to analog black holes

Abstract

Tidal Love numbers characterize the conservative, static response of compact objects to external tidal fields. Remarkably, these quantities vanish identically for asymptotically flat black holes in four-dimensional general relativity. This behavior has been attributed to hidden symmetries -- both geometric and algebraic -- governing perturbations in these space-times. Interestingly, a similar vanishing of selected multipolar Love numbers arises in the context of supersonic acoustic flows. These systems share several key features with black holes in general relativity, such as the presence of an effective acoustic horizon and a wave equation describing linear excitations. In this work, we explore a symmetry-based connection between the two frameworks and demonstrate that the ladder symmetries observed in acoustic black holes can be traced to structural properties of the underlying wave equation, mirroring those found in general relativistic black hole space-times.