Quote:
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Originally Posted by bachnga
When an clock falls into a black hole, its time rate, as viewed
by an external observer, slows down to a stop as it approach the
horizon.
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Yes, but it also being redshifted, and the redshift increases
faster and faster. The clock is actually accelerating toward
the black hole, and actually reaches the speed of light away
from you as it crosses your event horizon. Some people say
that to you it would appear to slow down and even stop, but
my understanding is that you will see the clock continue to
accelerate away from you even as its hands appear to stop.
You might see something like this, as the clock falls into a
supermassive black hole:
One second before the clock reaches your event horizon, it is
moving away from you at 10% the speed of light, and the hands
are slowed down noticeably. It is accelerating away from you
and becoming smaller with distance. Blue light from the clock
is shifted to green.
One tenth second before the clock reaches your event horizon,
it is moving away from you at 80% the speed of light, the hands
are hardly moving at all, and blue light is shifted to red.
The clock is becoming dim because the rate at which photons
from its face reach you is falling rapidly, like turning off
a light switch.
During the final hundredth of a second, blue light from the
clock face is shifted through the entire radio spectrum from
microwaves to short waves to long waves to waves too long to
detect with any existing device. It doesn't matter anyway
since the rate of photons reaching your receiver is orders
of magnitude too low to detect in any part of the spectrum.
The clock has become invisible to you. Though a few photons
may still reach you, they are too weak and too few in number
to detect.
As the clock disappeared, it was moving away from you at
virtually the speed of light, and still accelerating. The
distance between you and the clock was increasing in accord
with that speed.
Quote:
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Originally Posted by bachnga
If the black hole does not accumulate more matter, the event
horizon actually shrinks due to mass loss from to Hawking
radiation.
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Utterly negligible for this question, by many, many orders
of magnitude.
Quote:
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Originally Posted by bachnga
So the distance between the falling clock and the horizon
would increase, except the clock would fall further, but
would still go infinitely slow as it nears the horizon.
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The apparent speed of the clock away from you is not affected
by the relative time dilation which appears to slow the clock's
ticking. Not only does the clock not slow down, it continues
to speed up, without limit. Except that it disappears as it
reaches the speed of light.
Quote:
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Originally Posted by bachnga
1) Does an object falling into a non-growing black hole ever pass
the event horizon and actually enter the black hole interior?
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You see the clock fade out as it approaches your event horizon.
The clock sees the event horizon recede away from it, toward the
center of the black hole, but curve around it on the sides, so
that there is only a small circle of the outside Universe still
visible in the last moment before it gets too close to the
center and is spaghettified.
Never pass up an opportunity to use the word "spaghettified".
The FSM appreciates it.
Quote:
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Originally Posted by bachnga
2) Does an object actually enter by the event horizon expanding
to engulf the object?
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The increase in size of the event horizon is utterly trivial
in comparison to the size of the clock. The event horizon is
not really a surface, anyway. It is a deep, thick region in
which it is progressively more difficult for light to escape.
At the bottom -- what is called the "event horizon" -- light
has to be moving vertically away from the black hole to escape.
A little higher up, light can be moving at a slight angle and
still be able to escape. The farther up, the lower the angle
can be. At the "photon sphere" the light can move horizontally,
orbiting at a constant distance from the center. If the angle
is higher than horizontal, it will escape. Farther up yet, and
light can have a slight downward angle, and still escape from
the black hole. That progression continues to infinity.
Quote:
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Originally Posted by bachnga
Light and presumably gravity traveling parallel to the event
horizon surface must travel slow, as measured from the outside.
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I can't say anything about the speed of gravity, nor can I say
for sure anything about the speed of a photon moving away from
the black hole, but a photon travelling parallel to the event
horizon would not be slowed, as measured from the outside.
-- Jeff, in Minneapolis