  We study fluctuations and deformations of black branes over length scales
larger than the horizon radius. We prove that the Einstein equations for the
perturbed p-brane yield, as constraints, the equations of the effective
blackfold theory. We solve the Einstein equations for the perturbed geometry
and show that it remains regular on and outside the black brane horizon. This
study provides an ab initio derivation of the blackfold effective theory and
gives explicit expressions for the metrics near the new black holes and black
branes that result from it, to leading order in a derivative expansion.
