  We consider the theory of gravitational quasi-normal modes for general linear
perturbations of AdS4 black holes. Special emphasis is placed on the effective
Schrodinger problems for axial and polar perturbations that realize
supersymmetric partner potential barriers on the half-line. Using the
holographic renormalization method, we compute the energy-momentum tensor for
perturbations satisfying arbitrary boundary conditions at spatial infinity and
discuss some aspects of the problem in the hydrodynamic representation. It is
also observed in this general framework that the energy-momentum tensor of
black hole perturbations and the energy momentum tensor of the gravitational
Chern-Simons action (known as Cotton tensor) exhibit an axial-polar duality
with respect to appropriately chosen supersymmetric partner boundary conditions
on the effective Schrodinger wave-functions. This correspondence applies to
perturbations of very large AdS4 black holes with shear viscosity to entropy
density ratio equal to 1/4\pi, thus providing a dual graviton description of
their hydrodynamic modes. We also entertain the idea that the purely
dissipative modes of black hole hydrodynamics may admit Ricci flow description
in the non-linear regime.
