  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.
