So this is a fictional question since I am dumb to science yet trying to write up a science fiction playing in the far future...but still would need the understanding of some deeper physics to be able to set things up.
I have a scenario where a space station tested an onboard jumpdrive. The test failed and it sent the station to the wrong coordinates. It was appearing right near a black hole, and got into an outer orbit of it. It's systems were immediately deactivated, and the crew evacuated.
Now later, some people would come to it to salvage something from it that is very important to them. My question is, how would the reactivation of a stationwide artificial gravity, made by a core that creates a "fake mass" change the orbit of the station around the black hole? Would it be pushed outwards by having more gravity, or would it be tossed deeper inside, thus risking to reach the event horizon and never return? Which is more possible, or is it possible that there would be a constant change in balance where each could happen at any second? What do you think?