What do we mean by "stationary" perturbations? I know that black hole perturbations are related to gravitational waves and stationary means there should be no flow of energy. But this is vague. I am looking for a better understanding of what is the exact meaning of stationary perturbation in black hole physics. Can anyone help me with this? Thank you in advance!
A stationary perturbation of a black hole is a perturbation that is independent of time (or more technically a perturbation that is invariant under the time translation (Killing) symmetry of the black hole background).
This does imply that these perturbations cannot transport energy. However, some stationary perturbations of Kerr black holes are known to transport angular momentum. This is one reason why it is better to call these "stationary" rather than "static" perturbations.