We don't need no stinkin' . . . (Xmas Edition)
It is time to post my annual Christmas Black Hole puzzle. It’s pretty much the same puzzle every year, but since nobody ever gives me an answer I can understand, here is the latest version:
Two immortal and durable observers, call them Paul and Julio, want to observe the life history of a black hole. The strategy is this: Paul will stay back, where space-time is flat, but Julio will go in and stop just outside the horizon. Immortal though he is, Julio likes a cold one, so he drinks his beer and tosses the empty out the back window, where it falls freely (behind him) toward the black hole. Julio moves so close to the black hole that his watch runs very slowly compared to Paul’s. In fact he stops just at the point where one microsecond on his watch corresponds to T on Paul’s, where T is the time it takes for the BH to evaporate. By coincidence, that microsecond happens to be just the time it takes for the beer can drifting behind him to catch up and pass him on its way into the black hole.
After time T has passed, the BH has presumably evaporated and space-time is again flat, so Paul ought to be able to see and communicate with Julio again. A few zillion years have passed for Paul, but only that one microsecond for Julio, but now their clocks are on the same time again.
So what about the beer can? It was falling freely into the black hole when it caught up with Julio, but at that point, the BH had just finished evaporating. The distant observer and the nearby observer both saw the aluminum test body falling freely into the BH, but by the time it got there, they both agree that the BH was already gone.
But there is nothing special about the beer can, so how can anything fall into the BH, and, for that matter, how can the BH form at all?