Quote:
Originally Posted by m1omg
This is a popular misconception.It just appear to have not fallen, in fact it has already fallen there and so the gravitational field changes accordingly with increasing mass.
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There's a lot of misconceptions, but this is not one of them. Well, there are misconceptions about how it works and the meaning of it all. "Already fallen in". Well, GR plays some crazy games with temporal based notions such as "already".
In Schwarzschild coordinates, and indeed the coordinates based on the local ruler and clock of any external observer whose own world line does not itself cross the horizon, events past the horizon *never happen* in finite time. According to the simultaneity of all those external observers, the sense of where in their notion of space things are at their notion of "now", nothing ever crosses the horizon. Things only asymptotically approach it. The moment of horizon crossing occurs at t = infinity. Events past there *never happen*.
If you're on a world line that crosses the horizon, it happens in finite time and that world line terminates in short order at the singularity. But again, those events never happen in the frames of external observers. Events inside the horizon are causally disconnected, and this is how that plays out.
This is no problem for the external gravity. The more stuff falls in, the more mass is down there sitting frozen and gravitating externally. Additional mass leaves "more gravity behind" as it falls in.
And this violence to our Newtonian/Galilean notions of space and time is no restricted to real gravity. An accelerating observer perceives an event horizon behind which events never occur in his frame as well. An inertial observer perceives that as due to the fact that light beyond a certain point can only asymptotically catch that accelerating observer. Light can never reach him.
And that's the same thing inside a black hole horizon. Light can never get out to catch any external observers.
-Richard