Based on popular accounts of modern physics and black holes (articles, video lectures), I have come to understand the following:
- Black holes are predicted by General Relativity, a classical theory of gravity.
- We know that the universe is inherently quantum mechanical, so we believe General Relativity to be somehow incomplete or inaccurate.
- We do not have a quantum mechanical theory of gravity.
- We know that (on some level) General Relativity and Quantum Mechanics are incompatible.
- There is no direct experimental evidence of event horizons.
If all of these things are true (and if they aren't, please correct me), why do we trust black hole physics? How can we talk about something like Hawking Radiation if it uses both General Relativity and Quantum Mechanics and we know that we don't know exactly how to unify them.
When I read about or hear physicists talk about black hole related phenomena they speak with some considerable degree of certainty that these things actually exist and that they behave in the way the known physical laws describe them, so I'd like to understand why in the absence of direct evidence or a unified Quantum Mechanics/General Relativity framework we can be so confident in black hole physics.
EDIT: I just want to point out in response to some of the answers that I am aware of the evidence of very massive objects which are very compact and are believed to be black holes. I do not doubt that there exist very massive objects which have a great effect on the propagation of light and distort space and so on. When I talk about "black hole physics" I specifically mean physics which is derived by combining quantum mechanics and GR such as Hawking Radiation, things relating to the Information Paradox, etc. That's also why I specifically mentioned event horizons.