> 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.