General relativity has some mind-boggling consequences that seem to contradict special relativity (even though they really don't.)
For example, the GR equations allow (and in fact predict) for spacetime to expand and contract (so-called "metric expansion of space"). This has been pretty much confirmed to be happening to our universe, but it's also predicted to happen in other situations as well (such as close to a rotating black hole due to an effect called "frame dragging".)
The metric expansion of space has the counter-intuitive result that it allows, for example, for light (or anything else, really) to travel faster than c from a distant observer's point of view (even though locally the light never travels faster than c.) This does not break the theory of relativity (but on the contrary is predicted by it.)
This result is
so counter-intuitive that even some scientific papers on the subject mention its impossibility (without actually fully understanding the topic.) Some such papers, for example, express incredulity about the fact that stars/galaxies that are far enough from us are receding from us faster than c.
Frame dragging (another prediction of GR) is even harder to grasp. It causes for objects close to other, rotating very massive objects, to be seemingly "dragged" in the direction of the rotation. Because this is caused by the geometry of spacetime, rather than some force, there is no limit how fast (from an external point of view) the object may be dragged. In fact, the GR equations predict that there's a zone around rotating black holes where frame dragging is so strong that it causes particles to move faster than c (again, from an external POV; the particles themselves never exceed c locally, from their own POV.) This zone has been given the name "
ergosphere".
This in itself has some mind-boggling results. In theory if you had two rotating black holes close enough to each other, a particle could travel around them, inside both ergospheres in an 8-shaped path, that would cause it to travel back in time.