I am talking about this statement:You said you weren't talking about coordinate charts, but about physics. Physically, I've agreed several times that there is a line at the horizon (for a given angular direction in space), so that different infalling observers (or ingoing light rays) can cross the horizon at different events. Whether or not that line is covered by a given coordinate chart depends on the chart, so if you want an answer to your question exactly as you posed it, you'll need to specify which chart the coordinates you gave relate to.
So with actually you mean 'coordinates' and not 'physically'?For example, I asserted just now that the apparent "line" at the horizon in Schwarzschild coordinates is actually just a point--or, if we include the angular coordinates, what appears to be a 3-surface is actually just a 2-surface. How do I know this is right?
But I am confused by this statement:
Doesn't this say the opposite to what we now agree on?For example, in Schwarzschild coordinates, there appears to be an entire infinite line at the horizon, r = 2M, t = minus infinity to plus infinity, that actually, physically, is just a point