Let's imagine a stationary black hole and a fast moving object falling into BH. Let the momentum of the falling object be enough to give an observable bump to BH, pushing it into motion. Since the object does fall into BH, by momentum preservation BH should start moving. But I don't see how this could happen, because due to relativistic time dilation, the falling object never actually reaches the event horizon of the BH (from outside observer's point of view), let alone the singularity. So it seems that the empty space (or perhaps the gravitation field itself) is somehow able to transfer the falling object's momentum to the singularity, without even touching. Any ideas how this could be solved? Thanks.