  Perturbations of asymptotically Anti-de-Sitter (AdS) spacetimes are often
considered by imposing field vanishing boundary conditions (BCs) at the AdS
boundary. Such BCs, of Dirichlet-type, imply a vanishing energy flux at the
boundary, but the converse is, generically, not true. Regarding AdS as a
gravitational box, we consider vanishing energy flux (VEF) BCs as a more
fundamental physical requirement and we show that these BCs can lead to a new
branch of modes. As a concrete example, we consider Maxwell perturbations on
Kerr-AdS black holes in the Teukolsky formalism, but our formulation applies
also for other spin fields. Imposing VEF BCs, we find a set of two Robin BCs,
even for Schwarzschild-AdS black holes. The Robin BCs on the Teukolsky
variables can be used to study quasinormal modes, superradiant instabilities
and vector clouds. As a first application, we consider here the quasinormal
modes of Schwarzschild-AdS black holes. We find that one of the Robin BCs
yields the quasinormal spectrum reported in the literature, while the other one
unveils a new branch for the quasinormal spectrum.
