• Falling into a black hole

    From Stefan Ram@21:1/5 to All on Sun May 26 16:46:52 2024
    This might be a bit of a speculative question.

    They say that if an object falls into a black hole, it would appear
    to an observer at a great distance relative to the black hole that
    the object slows down but never actually reaches the event horizon.

    I'll refrain from pondering the idea that for an object near the
    event horizon, quantum mechanically due to the uncertainty principle,
    the probability of being inside the event horizon could already be
    greater than 0. I'm sure experts have thought about that as well.

    So, where was I? Ah yes, for an outside observer, the object reaches
    the event horizon only after an infinite amount of time has passed.

    On the other hand, from an outside perspective, the black hole
    itself could have evaporated after a finite amount of time AFAIK.

    What happens to the object, which from the outside appears
    to be waiting just short of the event horizon, after the black
    hole has evaporated from the point of view far from the black hole?
    Would we find the object outside the event horizon then? - TIA!

    [[Mod. note --
    A few comments (I suspect the author already knows these things):

    for an outside observer, the object reaches the event horizon only
    after an infinite amount of time has passed

    It's useful to think of the infalling object as sending out continuous
    light (or radio) signals.

    As the object approaches the event horizon, these signals take longer
    and longer to reach a (fixed) outside observer, and the signals are more
    and more redshifted. This results in the effect the author described,
    and means that the outside observer never sees any signals emitted on
    or inside the event horizon.

    It may be useful to rephrase the above-quoted statement as:

    Light/radio signals from the moment the infalling object crosses
    the event horizon will take infinitely long to reach, and will
    be infinitely redshifted when they arrive at, a (fixed) outside
    observer.

    This phrasing makes it clear(er) that the effects we're describing are
    caused by light/radio signal propagation near the event horizon, rather
    than the infalling object's motion being in any way arrested.

    Indeed, an observer riding the infalling object itself would measure it
    passing through the event horizon very quickly; it's "just" that after
    passing through the event horizon her light/radio signals would never
    reach the outside observer.

    The time scales are interesting: For a 1-solar-mass black hole
    (event horizon is a few kilometers in diameter):
    * outside observer sees the object's radio signals infinitely redshift
    and cut off on a time scale of microseconds; the last photon received
    by the outside observer will be very low-enegy (upon reception) and
    have originated just before the infalling object crossed the event
    horizon
    * infalling observer reaches r=0 singularity in microseconds
    (but any messages from her about what it's like, will never
    get to the outside observer)
    * outside observer sees the black hole evaporate in something
    on the order of 10^67 years

    As for your actual question, what happens to things inside a black
    hole when it (eventually) evaporates, it's a good question. Alas, I
    don't think we (yet) understand quantum gravity well enough to know
    the answer. :( There's a brief introduction to this topic at:
    https://en.wikipedia.org/wiki/Hawking_radiation#Black_hole_evaporation
    -- jt]]

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