  We study long-wavelength supersymmetric deformations of brane solutions in
supergravity using an extension of previous ideas within the general scheme of
the blackfold approach. As a concrete example, we consider long-wavelength
perturbations of the planar M2-M5 bound state solution in eleven-dimensional
supergravity. We propose a specific ansatz for the first order deformation of
the supergravity fields and explore how this deformation perturbs the Killing
spinor equations. We find that a special part of these equations gives a
projection equation on the Killing spinors that has the same structure as the
$\kappa$-symmetry condition of the abelian M5 brane theory. Requiring a match
between supergravity and gauge theory implies a specific non-linear
gauge-gravity map between the bosonic fields of the abelian M5 brane theory and
the gravity-induced fluid-like degrees of freedom of the blackfold equations
that control the perturbative gravity solution. This observation sheds new
light on the SUGRA/DBI correspondence.
