Near-horizon Carroll symmetry and black hole Love numbers

TL;DR

The note argues that the vanishing horizon-fluid velocity in the black hole membrane paradigm and the zero Love numbers of Schwarzschild black holes in $d=4$ GR can be understood from an emergent near-horizon Carroll symmetry. By identifying Carroll invariance on the horizon, the authors explain why the horizon fluid does not respond to tidal forces in the usual way. They connect this to tidal Love numbers using the ingoing-Eddington-Finkelstein gauge, showing that $v_a=0$ is equivalent to $k_{\rm el}=k_{\rm mag}=0$ for Schwarzschild BHs, while acknowledging that this does not extend universally to higher dimensions or alternative theories. The work suggests a symmetry-based angle on black hole tidal interactions and EFT descriptions, while highlighting the need for further study of how Carroll or BMS-type structures may influence BH Love numbers more broadly.

Abstract

According to the black hole membrane paradigm, the black hole event horizon behaves like a 2+1 dimensional fluid. The fluid has nonzero momentum density but zero velocity. As a result, it does not respond to tidal forces in the usual way. In this note, we point out that this unusual behavior can be traced back to an emergent, near-horizon Carroll symmetry (the Carroll group is the $c\rightarrow 0$ limit of the Poincaré group). For Schwarzschild black holes in $d=4$ general relativity, we relate the vanishing of the black hole fluid's velocity to vanishing of the black hole's Love numbers. This suggests near-horizon Carroll symmetry may have a role to play in explaining black hole Love numbers.