Here is the current state of evidence for black holes, from http://chandra.harvard.edu/chronicle/0307/onbh/
"Yet although thousands of bursts have been observed from neutron stars, not one has been observed from a black hole candidate. The lack of X-ray bursts from black hole candidates is a strong argument against the existence of gravastars and other exotic alternatives to black holes."
What "well established theories" do black holes contradict?
Black holes are predicted by relativity. How could they not be reconciled with it? http://en.wikipedia.org/wiki/Schwarzschild_metric