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

TL;DR

This paper investigates the hidden symmetries responsible for the vanishing of tidal Love numbers in black holes and draws parallels with similar phenomena in acoustic black holes, revealing structural similarities in their wave equations.

Contribution

It establishes a symmetry-based connection between black hole perturbations and acoustic flows, explaining the vanishing Love numbers through underlying structural properties.

Findings

Hidden symmetries explain Love number vanishing in black holes.

Analogies between gravitational and acoustic black holes are demonstrated.

Ladder symmetries in acoustic black holes mirror those in general relativity.

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.