  In this paper we establish energy decay for solutions to the Klein-Gordon
equation on the positive mass hyperboloidal anti-de Sitter Schwarzschild black
hole, subject to Dirichlet, Neumann and Robin boundary conditions at infinity,
for a range of the (negative) mass squared parameter. To do so we use vector
field methods with a renormalised energy to avoid divergences that would
otherwise appear in the energy integrals. For another region of the parameter
space, we use the existence of negative energy solutions to demonstrate linear
instability.
