alt Hacker NewsI figure at least some of it comes from the idea that mathematically, a singularity is a point (e.g., in the graph of z=1/w, there is a singularity at the point w=0, and in the graph of z=(1-w)²/(1-w) there is a removable singularity at w=1 (that is, the function is undefined at w=1, but if you put a point at (1,0), the graph will be continuous and no longer have any holes in it). The fact that both have the same name and the similar behavior of a black hole singularity to a mathematical singularity¹ can lead people to make an incorrect assumption.
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1. I must admit to a lack of sufficient GR education to feel confident in this, but I think that one of the issues that made physicists unwilling to accept the idea of black holes when they were first postulated was that there ended up being a division by zero in the mathematics.
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> 1. I must admit to a lack of sufficient GR education to feel confident in this, but I think that one of the issues that made physicists unwilling to accept the idea of black holes when they were first postulated was that there ended up being a division by zero in the mathematics.
Well, the Ricci curvature scalar blows up to infinity, which is obviously unphysical.
>The fact that both have the same name
They don't just have the same name, they are the same thing.
A Schwarzschild black hole has both: a removable singularity at the event horizon that is just an artefact of a particular choice of coordinates and a true non-removable mathematical singularity at r=0 where curvature really does go to infinity. It also wouldn't be much of an issue in classical physics, because this singularity is always hidden from outside observers, so the mathematical weirdness there can't screw with your normal predictions in space outside the black hole. The problems start once you consider quantum mechanics, because any such singularity will break unitarity (a fancy way of saying that probabilities must add up to 1), which means your theory as a whole can no longer make predictions. This has opened a whole can of worms with a bunch of solution attempts, which are all sadly untestable for the foreseeable future.