  We study the scattering of scalar waves propagating on the global monopole
background. Since the scalar wave operator in this topological defect is not
essentially self-adjoint, its solutions are not uniquely determined until a
boundary condition at the origin is specified. As we show, this boundary
condition manifests itself in the differential cross section and can be
inferred by measuring the amplitude of the backscattered wave. We further
demonstrate that whether or not the spacetime is stable under scalar
perturbations also relies on the chosen boundary condition. In particular, we
identify a class of such boundary conditions which significantly affects the
differential cross section without introducing an instability.
