A new instability of the topological black hole

We investigate the stability of massless topological black holes in ${{\rm{AdS}}}_{d}$ when minimally coupled to a scalar field of negative mass-squared. In many cases such black holes are unstable even though the field is above the BF bound and the geometry is locally AdS. The instability depends on the choice of boundary conditions for the scalars: scalars with non-standard (Neumann) boundary conditions tend to be more unstable, though scalars with standard (Dirichlet) boundary conditions can be unstable as well. This leads to an apparent mismatch between boundary and bulk results in the Vasiliev/vector-like matter duality.