Observing a mass forever approaching a BH, and BH growth

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stefanbanev said:
It was a rhetorical figure to make the point that "entire spacetime" (not a "spacetime") is the way to imply that even if the information about "event" can not be acquired by any means still may belong to realm of observer

What does "realm of observer" mean?

A spacetime (whether you qualify it with "entire" or not) is a perfectly well-defined concept in GR: it's a 4-dimensional manifold whose geometry is obtained by solving the Einstein Field Equation. Some solutions of that equation, like the Schwarzschild solution describing a static black hole, contain horizons; that's why it's not always the case that all events in the spacetime are visible from everywhere. But the horizons, and the events inside them, and the crossings of those horizons by infalling objects, are predictions of GR, a well-confirmed physical theory. They aren't just pulled out of thin air. So if you want to deny that those events will be part of spacetime under appropriate conditions, you have to find some way of explaining why these predictions of GR are somehow not correct. Just saying "I can't observe them so I don't believe they're there" isn't enough.
 
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PeterDonis said:
What does "realm of observer" mean?

A spacetime (whether you qualify it with "entire" or not) is a perfectly well-defined concept in GR: it's a 4-dimensional manifold whose geometry is obtained by solving the Einstein Field Equation. Some solutions of that equation, like the Schwarzschild solution describing a static black hole, contain horizons; that's why it's not always the case that all events in the spacetime are visible from everywhere. But the horizons, and the events inside them, and the crossings of those horizons by infalling objects, are predictions of GR, a well-confirmed physical theory. They aren't just pulled out of thin air. So if you want to deny that those events will be part of spacetime under appropriate conditions, you have to find some way of explaining why these predictions of GR are somehow not correct. Just saying "I can't observe them so I don't believe they're there" isn't enough.

Sure, agree on all accounts besides the last sentence that makes no sense for me. If I can not acquire information in principle about some events such events can not be qualified as "observables" yet, it does not preclude to include/incorporate such events into some model/theory as soon as such model/theory predicts correctly the outcome of experiments (the experiment's outcomes which I may qualify as observables).
 
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stefanbanev said:
Sure, agree on all accounts besides the last sentence that makes no sense for me. If I can not acquire information in principle about some events such events can not be qualified as "observables" yet, it does not preclude to include/incorporate such events into some model/theory as soon as such model/theory predicts correctly the outcome of experiments (the experiment outcomes which I may qualify as observables).
So are 'you' the arbiter of what prediction is an observable? These GR predictions are readily observable to someone else. Consider my example of retridiction in Solar system mechanics. We can retrodict what a past observer ought to have seen but we can't communicate with them to verify this. However most would say these retrodictions are observables for a past observer, rather than being in different category than predictions. We believe such retrodictions to the extent we believe the physical theory. Similarly for GR predictions about the horizon crossing observers.
 
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PAllen said:
So are 'you' the arbiter of what prediction is an observable? These GR predictions are readily observable to someone else. Consider my example of retridiction in Solar system mechanics. We can retrodict what a past observer ought to have seen but we can't communicate with them to verify this. However most would say these retrodictions are observables for a past observer, rather than being in different category predictions. We believe such retrodictions to the extent we believe the physical theory. Similarly for GR predictions about the horizon crossing observers.

It seems a rephrasing what I said above (I like my version more ;o)...
 
stefanbanev said:
It seems a rephrasing what I said above (I like my version more ;o)...
No, I think we disagree. I say the observables of a theory are things that could be observed by some observer. You say the observables of a theory are things that could be observed by you.
 
stefanbanev said:
If I can not acquire information in principle about some events such events can not be qualified as "observables" yet

You're not the only observer in the universe. An observer who falls into the black hole can see events behind the horizon just fine.