  We show that the emergent near-horizon conformal symmetry of extremal black
holes gives rise to universal behavior in perturbing fields, both near and far
from the black hole horizon. The scale-invariance of the near-horizon region
entails power law time-dependence with three universal features: (1) the decay
off the horizon is always precisely twice as fast as the decay on the horizon;
(2) the special rates of $1/t$ off the horizon and $1/\sqrt{v}$ on the horizon
commonly occur; and (3) sufficiently high-order transverse derivatives grow on
the horizon (Aretakis instability). The results are simply understood in terms
of near-horizon ($\mathrm{AdS}_2$) holography. We first show how the general
features follow from symmetry alone and then go on to present the detailed
universal behavior of scalar, electromagnetic, and gravitational perturbations
of $d$-dimensional electrovacuum black holes.
