One of the big mysteries about the black hole at the center of the galaxy is, 'Why don't we see emission from matter falling onto the black hole, or, rather, the black hole eating up its surroundings?'
As an astronomer, I get to ignore the details of the things that we dont understand. Theres a lot of work that we can do on scales that we do understand, and there is actually a finite size that I can associate with a super massive black hole.
Black holes are very exotic objects. Technically, a black hole puts a huge amount of mass inside of zero volume. So our understanding of the center of black holes doesn't make sense, which is a big clue to physicists that we don't have our physics quite right.
The question that I started off with was, I thought, very simple. It was just 'Is there a massive black hole at the center of the Milky Way?' But one of the things I love about science is that you always end up with new questions.
An ordinary black hole is thought to be the end state of a really massive star's life.
How do you observe something you can't see? This is the basic question of somebody who's interested in finding and studying black holes. Because black holes are objects whose pull of gravity is so intense that nothing can escape it, not even light, so you can't see it directly.