Mathematician Kelsey Houston-Edwards, guesting on PBS Space Time, agrees the singularity at a black hole's centre is real rather than a coordinate artefact. She notes that infinities in a model have often signalled a flawed theory.
…to space-time viewers is the event horizon of the black hole. I'll leave that to you to explain. Here on Earth, the North and South Pole are examples of coordinate singularities. It's possible to pass through time zones infinitely quickly, but only because of your choice of spherical coordinates.
Alright, that makes sense. But the gravitational singularity at the center of a black hole is a so-called real singularity, right? I mean, the curvature and the density are infinite from any frame of reference.
Right. And there's no way to avoid a horrible crushing death just by switching coordinate systems. But the reality of the black hole singularity may give reason to doubt the theory that predicts such a thing. In fact, it's happened many times before. From models of the movement of water to human population growth, mathematics predicts a physical singularity and we've been forced to reject the corresponding theory.
So you're saying Einstein is wrong? Blasphemy. Actually, Einstein himself agreed on this point. Guys, you should check out Kelsey's show Infinite Series, where she goes into much more depth on the nature of singularities. It's a math show, by the way, so it's sometimes about real stuff.
Mathematicians are lucky. Being limited by reality is so boring.
So, does the fact that it includes a singularity mean there's something fundamentally wrong with Newton's law of gravitation? Well, we already know the law isn't really so universal. When the gravitational field is too strong, say near a star or a black hole, Newton's law gives the wrong answers…