Sorry, you are still arguing against things I never said or that you desperately want to misinterpret in a disingenuous way. If I was actually wrong about anything I said, all you had to do was write down the explicit metric and point out exactly where it disagrees with what I said. But if you did, you would immediately see that your argumentation falls apart.
> you are still arguing against things I never said
You said the singularity is a point in space. That's what I'm arguing against.
The rest was an attempt to try to help you understand the correct physics. Evidently it was wasted effort. I won't do it again.
> all you had to do was write down the explicit metric and point out exactly where it disagrees with what I said.
Sure, it's the one in terms of t' and r in the Wikipedia article on Eddington Finkelstein coordinates. [1]
> if you did, you would immediately see that your argumentation falls apart.
No, I see that yours does.
The article is using the timelike signature convention, so positive ds^2 is timelike and negative ds^2 is spacelike. Vertical lines in a spacetime diagram (like the one just a little bit below the metric, on the right, that shows the light cones) are intervals where only dt' is nonzero. It is obvious from the metric that for any r < 2M, i.e., anywhere inside the horizon, such intervals give a negative ds^2, since 1 - 2 GM / r is negative. So vertical lines, of which the singularity is one, are spacelike, and t' is a spacelike coordinate inside the horizon (just as r is). And a spacelike line cannot be a point in space. It can only be a moment of time. The fact that it is vertical on the diagram does not change that.
