Near-horizon Carroll symmetry and black hole Love numbers

TL;DR

This paper links the near-horizon Carroll symmetry of black holes to their fluid-like horizon behavior and the vanishing of Love numbers, offering a new perspective on black hole responses to tidal forces.

Contribution

It identifies the near-horizon Carroll symmetry as a key factor behind the black hole horizon's fluid properties and the zero Love numbers in Schwarzschild black holes.

Findings

Near-horizon Carroll symmetry explains horizon fluid behavior.

Vanishing Love numbers are related to zero fluid velocity.

Symmetry considerations may elucidate black hole tidal responses.

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 Poincar\'e 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.