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According to the no-hair theorem a black hole can be completely characterized by three parameters: mass, electric charge, and angular momentum. Can any of these parameters be determined by an observer who is inside the event horizon of the black hole?

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  • $\begingroup$ Can you clarify what you mean by "observer"? Example: Is this question equivalent to asking whether the metric outside the horizon can be completely inferred from complete knowledge of the metric inside the horizon? Or are you asking about some kind of localized observer whose observations are limited to a neighborhood of a timelike geodesic? $\endgroup$ Commented Oct 27, 2020 at 22:45
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    $\begingroup$ @ChiralAnomaly By an observer I mean a person who can make observations, perform experiments and make measurements. I think the metric outside the event horizon can be completely inferred given complete knowledge of the metric inside the horizon. However I'm not sure if the metric inside the event horizon can be completely determined by an observer inside the event horizon. Example: Can a person inside the event horizon determine the angular momentum of the black hole? $\endgroup$
    – Andrew
    Commented Oct 28, 2020 at 0:08
  • $\begingroup$ @Andrew "I think the metric outside the event horizon can be completely inferred given complete knowledge of the metric inside the horizon." - This is not true in general. For example, the metric inside a collapsing shell is always flat and gives you no idea of the metric outside. For more options see this: What's inside a frozen star? $\endgroup$
    – safesphere
    Commented Oct 28, 2020 at 21:10
  • $\begingroup$ @safesphere The metric inside a collapsing shell which forms a black hole is only flat until the shell collapses to the radius of the observer, which happens in a finite time for an observer inside the event horizon. $\endgroup$
    – Andrew
    Commented Oct 29, 2020 at 8:07
  • $\begingroup$ It goes without saying that the observer within the event horizon is part of the black hole. $\endgroup$
    – EvilSnack
    Commented Nov 20, 2021 at 2:16

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Can any of these parameters be determined by an observer who is inside the event horizon of the black hole?

Yes. As long as they can make non-local observations (i.e. they are not confined to a small windowless spaceship) then an observer inside the event horizon can in principle gather just as much information about the black hole as an external observer. If anything, they might have more information than an external observer because they may have a less distorted/red-shifted view of other objects that have passed the event horizon.

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