Einstein originally thought that black holes were simply an mathematical artifact, and not possible in reality.
Since then, we have observed objects that look a lot like we would expect black holes to look. There are theories, such as this one, that describe those objects as something different than what GR proposes, but thus far no testable prediction has contradicted GR's version.
Part of the problem is that many of the differences are about the interior of the event horizon. At least under GR's model, such differences are nit observable, even in principle.
Since then, we have observed objects that look a lot like we would expect black holes to look. There are theories, such as this one, that describe those objects as something different than what GR proposes, but thus far no testable prediction has contradicted GR's version.
Part of the problem is that many of the differences are about the interior of the event horizon. At least under GR's model, such differences are nit observable, even in principle.