  It is well known that asymptotically flat Schwarzschild black holes in
general relativity in four spacetime dimensions have vanishing induced linear
tidal response. We extend this result beyond linear order for the polar sector,
by solving the static nonlinear Einstein equations for the perturbations of the
Schwarzschild metric and computing the quadratic corrections to the
electric-type tidal Love numbers. After explicitly performing the matching with
the point-particle effective theory at leading order in the derivative
expansion, we show that the Love number couplings remain zero at higher order
in perturbation theory.
