  The 4D-5D connection allows us to view the same near horizon geometry as part
of a 4D black hole or a 5D black hole. A much studied example of this
phenomenon is the BMPV black hole uplifted to 6D with flat base space versus
Taub-NUT base space. These black holes have identical near horizon AdS_3 x S^3
geometry. In this paper, we study modes in AdS_3 x S^3 and identify those that
correspond to supersymmetric hair modes in the full black hole spacetimes. We
show that these modes satisfy non-normalisable boundary conditions in AdS_3.
The non-normalisable boundary conditions are different for different hair
modes. We also discuss how the supersymmetric hair modes on BMPV black holes
fit into the classification of supersymmetric solutions of 6D supergravity.
