One possible way to directly infer black hole properties is by observing the sort of event discussed in today’s paper: the tidal disruption of an individual star after a close approach to a supermassive black hole.
A theoretical study of what we can expect to see when a hot Jupiter crashes into its host star.
Small daily flares are observed from the black hole in the center of our galaxy. The authors of this paper propose the flares are due to Sgr A* frequently snacking on asteroids!