  Recent developments in the gravitational waves interferometry require more
pertinent theoretical models of gravitational waves generation and propagation.
Untouched possible mechanisms of spin-2 spacetime perturbations production, we
will consider their subsequent scattering on other black holes (BHs).
Specifically, we consider a generalization of the Regge-Wheeler-Zerilli
equations for the case of distorted BHs (BHs surrounded with matter) in
Minkowski and Anti-de Sitter spacetimes, the metric potential of which obeys
the Liouville equation. We establish significant differences in scattering
characteristics of waves of different spins and angular momenta, including the
gravitational waves, caused by losing the spherical symmetry of their
propagation background. In particular, we demonstrate the strong impact of the
background geometry deformation on the grey-body factors, hence on the
absorption cross-sections of scattering waves, and explore the issue of
stability of the background geometry upon changing the deformation degree
parameters.
