B What (if anything) limits the speed of something falling into a black hole?

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PAllen

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The point of view you choose shouldn't affect the reality of the physics, should it? I mean even if different observers have different perspectives there should be some calculable "reality" as to what happens which all should agree on when spacetime distortions are considered. Can't there be one chart in some sense that can be translated into any reference frame or is that physically unrealistic? (neglecting quantum effects)
Yes, any chart that spans the horizon may be used, and all will make identical physical predictions. Peter has suggested a convenient coordinate chart to use and provided a link (for the idealized non rotating BH).

Another less commonly used chart that I happen to like is the Lemaitre chart:

https://en.wikipedia.org/wiki/Lemaître_coordinates

These have the feature of maintaining 1 timelike and 3 spacelike coordinates throughout the exterior and interior (Gullestrand-Panlieve coordinates are all spacelike inside the horizon). Kruskal coordinates also maintain 1 timelike and 3 spacelike coordinates everywhere, but I find them harder for many computations. In Lemaitre coordinates, free fall trajectories from infinity have a very simple representation, and the time coordinate gives proper time along such trajectories.
 
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In Lemaitre coordinates, free fall trajectories from infinity have a very simple representation, and the time coordinate gives proper time along such trajectories.
How would I hook that to a white hole?
 

PAllen

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How would I hook that to a white hole?
Lemaitre coordinates don't include the white hole portion of the full Kruskal geometry. They include two of its 4 quadrants. This is not a bad thing because there are good reasons to believe the the other two quadrants don't exist in our universe. This is because there is no evolution from a prior state not in including them, that can result in their existence. A BH formed by collapse includes only geometry of the type covered by Lemaitre coordinates.
 
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This is because there is no evolution from a prior state not in including them, that can result in their existence.
Why not?
 
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I seem to have a system in my head where the entire universe (a white hole for argument sake) pushing in on every system in the universe (especially black holes) what can't work mathematically...
 

PAllen

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Because it is a mathematical theorem? Not sure what you are looking for, but a white hole can only exist as an eternal object. If anything like FLRW cosmology is true, white holes are impossible because the initial state doesn't include them.
 
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I seem to have a system in my head where the entire universe (a white hole for argument sake) pushing in on every system in the universe (especially black holes) what can't work mathematically...
Well, nothing can work mathematically without doing the math. Please see the professional literature for that, we don't accept personal speculation here.
 
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