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Comment by quantadev | Hacker News Reader

Nobody knows what happens at the event horizon, but we do know from the perspective of an outside observer things about physics 'break'. It makes sense that there's a flip-side to that 'breakage' (on the inside of the surface, or even "only at" the surface) that isn't just normal space as if nothing happened.

For example there's no mathematics at all that mankind has ever known where an asymptotic approach towards some limit doesn't have a mirror version (usually inverted) on the other side of the asymptote. If we see time stop, at the EH it seems wrong to assume there's nothing "stopped" similarly from the other side too. So this means the surface has to be very special. You don't just pass by it and not notice as you fall in, imo.

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> For example there's no mathematics at all that mankind has ever known where an asymptotic approach towards some limit doesn't have a mirror version (usually inverted) on the other side of the asymptote.

That’s a strong statement. 1/sqrt(x), over the reals, doesn’t have an inverted world for x<0. Maybe you could argue that it does exist, weirdly rotated, outside the reals?

In any event, the Schwarzchild metric itself is an actual example of this. From the perspective of a doomed spaceship at the event horizon, the Schwarzchild metric is quite civilized.

The stuff after the horizon is a different story, but that’s not immediately after crossing the event horizon — it might be whole nanoseconds later :)

Go take a GR class. It’s fun and mind-bending.

What I meant to say was "asymptotically approaches infinity" for 'f(x)' at some limiting value 'x' and thus a left/right mirroring of the function. I shouldn't assume people know I mean vertical just because I say asymptotic, so thanks for catching that imprecision in my wording.

As you probably know, horizontal asymptotes are never what we think of as the 'problematic' parts of Relativity, because when something approaches a constant that's never something that breaks the math.

The Schwarzchild metric, being a relationship of 6 different variables I think, has some relationships that go to infinity asymptotically at the EH radius and some things that approach a constant at that radius, so it's an example of the kind of asymptotic I was talking about _and_ one like your "horizontal" example.

1/sqrt(x) is a vertical asymptote?

Replace "is a" with "has one".

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