  Initial conditions given on a spacelike, static slice of a non-globally
hyperbolic spacetime may not define the fates of classical and quantum fields
uniquely. Such lack of global hyperbolicity is a well-known property of the
anti-de Sitter solution and led many authors to question how is it possible to
develop a quantum field theory on this spacetime. Wald and Ishibashi took a
step towards the healing of that causal issue when considering the propagation
of scalar fields on AdS. They proposed a systematic procedure to obtain a
physically consistent dynamical evolution. Their prescription relies on
determining the self-adjoint extensions of the spatial component of the
differential wave operator. Such a requirement leads to the imposition of a
specific set of boundary conditions at infinity. We employ their scheme in the
particular case of the four-dimensional AdS spacetime and compute the
expectation values of the field squared and the energy-momentum tensor, which
will then bear the effects of those boundary conditions. We are not aware of
any laws of nature constraining us to prescribe the same boundary conditions to
all modes of the wave equation. Thus, we formulate a physical setup in which
one of those modes satisfy a Robin boundary condition, while all others satisfy
the Dirichlet condition. Due to our unusual settings, the resulting
contributions to the fluctuations of the expectation values will not respect
AdS invariance. As a consequence, a back-reaction procedure would yield a
non-maximally symmetric spacetime. Furthermore, we verify the violation of weak
energy condition as a direct consequence of our prescription for dynamics.
