  We study the near-zone symmetries of a massless scalar field on
four-dimensional black hole backgrounds. We provide a geometric understanding
that unifies various recently discovered symmetries as part of an SO(4,2)
group. Of these, a subset are exact symmetries of the static sector and give
rise to the ladder symmetries responsible for the vanishing of Love numbers. In
the Kerr case, we compare different near-zone approximations in the literature,
and focus on the implementation that retains the symmetries of the static
limit. We also describe the relation to spin-1 and 2 perturbations.
