>>Dark matter is escaping the black hole much faster than the speed of light.
If it has mass, then it can't be moving as fast (or faster) than the speed of light.
>>Perhaps this leaves a wake that we can detect.
You'd need some sort of medium for a 'wake' to be apparent... there *are* gravity waves that are detectable, but they are created by massive objects moving through space.
>>If dark matter is escaping from all sides of the black hole equally, it may not
>>leave an observable wake or push back.
Not sure what this means... and, why would dark matter (or, regular matter in any case) be moving away from a black hole? There are jets of accelerated matter shooting out from the black hole, that the black hole itself has accelerated, but these aren't moving at the speed of light.
>>But perhaps you can imagine a scenario where the distribution of dark matter escaping
>>the black hole is not equal, leading to a wobble or the black hole being pushed one direction or another.
I just don't know why matter would be *leaving* a black hole if it wasn't accelerated through the jets...
>>I hear that Sag A moves around a lot or maybe that is just it's plume that moves a lot compared to M87
>>which is much more massive.
I haven't heard this... I know there are some stars that orbit Sag A*, and they're accelerated to very high speeds at closest approach.
>>I believe dark matter escapes from black holes in a curved motion. Perhaps that helps with detection
We haven't ever isolated dark matter to know what it is - or, even if it truly exists. Since black holes have immense gravity very close in, I would doubt even dark matter would be able to escape...