What's so impressive here is just how much it's possible to get wrong in a single headline. Black holes, of course, don't have 'shadows.' I think what they mean is its event horizon, though the article is so fuzzy it's difficult to be sure.
However, the real shocker is the apparent claim that general relativity is dead. Here's the thing. No it isn't. What the article actually says is that if a black hole's 'shadow' (event horizon?) isn't perfectly spherical or isn't just the right size for it's mass, then general relativity's predictions would be wrong. Well, duh. This would also be true if it were pink or singing the Stars and Stripes. Note however, that no one has discovered that its shape or size is different from prediction. (Or that it's pink.) They're just saying that we might be close to being able to make a measurement to see if it lives up to prediction. That's all.
Even if there is a disparity, as the article says 'If Einstein is wrong, general relativity won’t go away—it’s too good at what it does. It just won’t be the whole story anymore.' Right. And that fits with the headline how?
I appreciate editors want headlines that grab people's attention, but if they are going to deviate so far from the facts in order to do so, why not go the whole hog? I look forward to the headline on an article about a new extrasolar planet, where the story is that it's about the right size for life to read:
NEW PLANET HOME TO KILLER BEES, PROVED TO BE THE UNIVERSE'S BIGGEST COLDPLAY FANS.
Why not? It makes as much sense.