1st point: black holes CAN move. the evidence is all about the universe--there are plenty of binary systems (solar systems w/ 2 stars) where one star has collapsed into a black hole and both the black hole and the visible star are wheeling around each other.
2nd point. when the two stars (visible/black hole) are wheeling around each other, it's possible to determine the "mass" of the black hole based on the orbits of the two. i don't think this can really be called information "escaping" from the black hole--if that's considered information, then the emission of x-rays from the black hole would have to be considered some kind of information as well. similarly, even if an indestructible neutron star were to hit the black hole and cause it to bobble, i don't think that would be considered information being leaked.
3rd point. from our point of view, watching this indestructible neutron star, as the star approaches the event horizon, it will appear to move slower and slower, due to special relativity. even after infinite time, it will NOT EVER appear cross the event horizon. so the point is moot.
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oh baby oh baby, i like gravy.
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