Near-horizon Carroll symmetry and black hole Love numbers

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 $c\to 0$ 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.

4 pages

Cited by in corpus (8)

• Tidal Love Numbers of Kerr Black Holes
• Static response and Love numbers of Schwarzschild black holes
• Ladder Symmetries of Black Holes: Implications for Love Numbers and No-Hair Theorems
• Conformal Carroll Scalars with Boosts
• Carrollian hydrodynamics from symmetries
• Carrollian manifolds and null infinity: A view from Cartan geometry
• Heavy-ion collisions, Gubser flow, and Carroll hydrodynamics
• Renormalization of conformal infinity as a stretched horizon