Now, my next question would be, in those "weight on a sheet" analogies, you place a weight on the sheet and it only sinks down so far. Is there a point where enough weight on a small enough area would cause the object to keep sinking? e.g. imagine space-time as infinitely pliable play-dough, and on a thin sheet of it you can place light objects that only sink in a bit but stay. A heavy enough object would sink and just keep going, slowly at first but picking up speed as it goes. Normally, a thin sheet of play-dough would tear at this point and the object would just drop through. But say this is infinitely pliable and will just keep stretching as the object sinks. This creates steeper and steeper slopes in a small area around it, and exponentially increases surface area.
Now, imagine that the rest of the sheet gets drawn down a bit, too. Like, say, an artesian well drawing down the water table. Near the well, slopes are steep and asymptotic at the center. Further from the well, even at great distances, the water table is drawn down only a tiny amount, but still influenced by the well.
If you were at some point outside the "event horizon", where the slopes are steep, but still within the area of influence for the draw down effect, you would see the surface area all around you grow exponentially as the object at the center sinks ever further. Despite not being close enough to tumble down the slope.
Could the expansion of the universe be influenced by some giant ultramegasuperdupermassive black hole "drawing down" the fabric of the universe around it, stretching it faster and faster as time goes on, and we're somewhere in the middle of one of the side slopes (but not within the event horizon), observing the increase of surface area as a result?
Then again, if that were the case, we'd observe expansion in only two directions: toward and away from the center. But expansion is probably being observed in all directions equally. Unless we are in the event horizon and are looking up out of our hole as we sink deeper, observing everything getting further away as we go.
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