Hello. I've had a question in the back of my mind about black holes for a while now. I asked my astronomy professor (who's a pretty smart guy), and he basically said that since he's not an expert on black holes, there's a lot about them that even he doesn't understand and he didn't know the answer to my question.

So it goes like this: As you fall towards the event horizon of the black hole, time dialation will slow down the passage of time. Or, for the unfortuante infalling astronaut, he will see the time for the rest of the universe speed up. Now the equations work out such that time dialation becomes infinte at the event horizon. This means that for any outside observer looking at a black hole, infalling matter will take an infinite amount of time to reach the even horizon of the black hole.

This is more then just an optical illusion, however. The personal time of infalling matter is actually slowing down (please note that I have no problem with this, my question is still coming ). Now, normally this wouldn't be a problem. The infalling matter may take longer to reach the black hole (it'll take forever in fact), however it will still be adding it's mass to the overall gravitational well of the black hole. A spacecraft orbiting the black hole won't notice a difference in it's orbit weather the matter is hovering a few millimeters about the event horizon or actually inside it.

We also know that black holes can evaporate. While this takes an extremly long time to happen, It still takes much less time then infinity. So here is my question:

If it takes an infinite amount of time for a chunk of matter to reach the event horizon of a black hole, and the black hole will evaporte completely in less time then that, wouldn't that mean that any matter falling towards a black hole won't acutally reach the event horizon? The black hole should evaporate completely before you ever get there!

Anyone have any thoughts on this?

Is it the event horizon or the singularity that it takes a long time to reach. Since there would be no black holes if this effect applied at the event horizon, my guess is that it must be the singularity.

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For those inclined to oppose human meddling with the structure of the universe or the composition and configuration of objects and groups of objects within the universe, consider:
Whether there is a limit to the magnitude of a modulation of chaos below which order remains invariant? Or, is order but a fiction invented by perspectives applied over finite, however large, time intervals?

That isn't true. Time dilation is something which is seen by
an observer in a different state of motion or in a different
gravitational potential from whatever he is observing. If I
am the dumb astronaut falling into the black hole, and you are
the smart astronaut watching me from a good distance away, you
will see me time-dilated and redshifted. If you were even
dumber than me, and came with me into the black hole, leaving
nobody behind to tell the sad story or return our spacecraft to
the rental shop, we would not see each other time-dilated or
redshifted.

That isn't accurate, either. If I fall into the black hole
from a good distance away, I will be moving at very nearly the
speed of light relative to you as I cross the event horizon,
and I will be accelerating downward away from the light which
is coming into the black hole after me. I say "away from" but
I didn't mean to imply that I'm getting farther from the light--
I'm not-- but I'm moving fast enough that I will reach the
singularity before the light can reach me. On the other hand,
if I were to slow my fall into the black hole somehow, so that
I was falling at much less than the speed of light as I crossed
the event horizon, then you *would* be right: The rest of the
Universe would appear to be speeded up.

Only relative to a distant observer. The infalling matter sees
rapid acceleration to the singularity, accompanied by gratuitous
spaghettification.

That pretty well obviates your main question.

-- Jeff, in Minneapolis

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"The other planets?
Well, they just happen to be there, but the point of rockets is to explore them!"
-- Kai Yeves

Gourdhead -- it applies to the event horizon.


Jeff Root -- I'm aware that time dialation is relative, and the infalling astronaut doesn't see his own time as running slower. I'm talking about an outside observer watching the infalling astronaut will see the infalling astronaut's time run slower, and will witness that it takes forever for the infalling astronaut to reach the event horizon.

But I think your wrong that the time dialation is only an illusion, and even though we don't see the astronaut ever cross the event horizion in reality he already has. Because consider that we watch him for 1000 years getting ever closer to the black hole. Then, he decides to turn around and come back (or perhaps he was on a trajectory that only had him orbit very close to the event horizon and then swing back). At any rate, the astronaut may have only experienced 3 or 4 seconds, but the rest of the universe has still aged 1000 years. It's not like the astronaut falls in, 3 seconds later turns around and comes back and only 3 seconds has passed for the rest of the universe even though we're still seeing an image of him falling into the black hole.

If you see him falling into a black hole, and 1000 years later you still see him falling into the black hole that's because he's still falling into the blackhole. He hasn't crossed the event horizon yet, in either your reference frame or his. So this doesn't invalidate my question.

I didn't call what a distant observer sees an "illusion".
That is highly misleading. What the distant observer sees is
light from the falling object. Light from a falling object
naturally is not the same as the falling object.

Whoa! Whoa! Whoa! Nothing like that can happen.

Let's say we are talking about a supermassive black hole, with
a mass equal to millions of solar masses. That means it will be
comparable in size to the Solar System. Maybe out to the orbit
of Saturn, or Uranus? Somebody should come along with an actual
set of numbers. This large size makes things easier for us to
deal with. The gravitational well is spread out, which means it
strongly affects a large volume of space, and tidal forces at the
event horizon are vastly lower than in a stellar-mass black hole.
It would actually be possible for a spacecraft to cross the event
horizon without being immediately spaghettified.

You are orbiting several light-weeks away, out of danger. You
have the new, improved SuperDuper UltraMega HyperDiaperScope,
capable of seeing my spacecraft at that distance. *

I get as close as possible to the black hole without falling in,
just swinging around it and firing my engines furiously to keep
from actually being sucked in. (Black holes really suck if you
get close enough.) You see me whizz across the black background
at very nearly the speed of light. I and my spacecraft are
seriously squished in your view by the relative speed. Light
and signals from my spacecraft are highly redshifted.

I'm not sure what more I can accurately and usefully say about
that scenario, so let's switch to a slightly different one.

I fall straight into the black hole. You watch me fall in.
Again, light and signals from me are more and more redshifted as
I get closer and closer to the event horizon. We have calculated
the exact nanosecond (in my reference frame) that I will cross
your event horizon. (The location of the event horizon depends
on your distance from the black hole and your relative motion.)
The clock I am holding up for you shows my proper time. It will
be 12:00:00.00 at the instant I cross your event horizon. You
see it read 11:59:59.00 and it is obviously slowing. It is also
getting dim despite the powerful lights inside my spacecraft, as
the rate photons are reaching you decreases. A second later you
see my clock reading 11:59:59.90, but it is very dim and grainy,
and extremely redshifted. A second later you can barely make out
that my clock reads 11:59:59.98. A second after that, you see
only a handful of photons which were redshifted into the radio
portion of the spectrum. And a few photons a second after that.
That's it. You watch for five more days, and nothing. The last
second of light from me that you could detect lasted maybe four
seconds for you at most. The rest was redshifted so much that
it didn't contain enough information to determine whether it was
signal or just noise, even with the new, improved SuperDuper
UltraMega HyperDiaperScope. *

For a supermassive black hole, one light-hour in radius, it
would take roughly one hour of my proper time for me to fall
from your event horizon to the singularity. I would be
spaghettified shortly before reaching the singularity.

For a stellar-mass black hole, two or three miles in diameter,
I would be spaghettified before you saw me reach the event
horizon, and it would take only microseconds of my proper time
after that for my atomized remains to reach the singularity.

You are going to see events-- and me-- stretched out some,
but within a second or two, the rate at which photons from me
reach you will have fallen so low that there will no longer be
any detectable signal. Only a finite number of photons leave
me in my last second before crossing your event horizon, and
more and more of those photons fall into the black hole rather
than escaping, so I disappear pretty quickly. And as I've
repeatedly said, those photons are redshifted, so they have
less energy when they reach you than when they left me. Lots
of reasons for me to vanish quickly.

And I'll repeat that all you are seeing is the light from me--
not me. I'm long gone by the time the light reaches you.

-- Jeff, in Minneapolis

* SuperDuper UltraMega HyperDiaper and SuperDuper UltraMega
HyperDiaperScope© Copyright 2006 by Jeff S. Root.

The SuperDuper UltraMega HyperDiaper is a full metal diaper.

__________________
http://www.FreeMars.org/jeff/

"The other planets?
Well, they just happen to be there, but the point of rockets is to explore them!"
-- Kai Yeves

Not correct. He appears to have not crossed the event horizon as seen by the distant observer, but he certainly does & will cross the event horizon in his own reference frame. His failure to cross the event horizon is only an illusion.

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Don't try this at home - We're what you call "professionals" - MythBusters.

I think the question is well posed though, as nothing (but light, I think. Ask Grey) ever does cross an event horizon in the sense of time measured here on Earth (it is more than an illusion, it is real, for us here). How that connects with Hawking radiation is tricky, I think it has been visited before, maybe on the FAQ.

The general opinion so far seems to be that my failure to see the astronaut cross the event horizon is only an illusion. Meaning that I don't see him cross, but that's just a trick of light due to the gravity well of the black hole. In reality, he's already crossed it. That correct?

If so, I have a problem with this. Because lets say he's not going to cross the event horizon, just get REALLY close and then come back (certainly possible). He basically gets so close that millions of years later I will still see him near the event horizon. However, from his point of view this encounter only takes maybe an hour. So, he goes way down into the gravity well of the black hole and then comes back to the rest of the universe. Now, if my preception of him slowing down is merely an illusion, then he should be able to come back to me and say hi an hour later even though I still see him falling in. But this isn't what happens. If he gets that close to the event horizon and then comes back, he will discover that millions of years has passed by for the rest of the universe.

Now assuming that that is true (and I'm pretty sure that it is), then it seems like as he's falling in time is actually slowing down for him, so that if I see him take a million years to get to a spot A, one million years later he will actually be at spot A, not just an image of him. Likewise, a billion years later when I see him a fraction of a nanometer above the event horizon, he's actually a fraction of a nanometer above the event horizon, and so on. Where am I going wrong with this view?

Also, going back to the classic example of the astronaut sending signals to use that get progressively further apart, is it that the light actually takes longer to climb out of the gravity well of the black hole? I thought that since light MUST travel at 300,000 km/s, then it just got extremely redshifted as it climbed out. So if I'm one light hour away, then the light will only take an hour to get from the astronaut to me regardless of how close to the event horizon he is. Or am I wrong on this?


Jeff -- Why not? And which part exactly are you refering to? Keep in mind that when I said "getting closer to the black hole", I'm refering to the event horizon of the black hole and not the singularity. Sorry if that's what confused you (I should have stated it clearer).

Hi, welcome to the forum, Astrowannabe.

Not necessarily, it seems.

It doesn't take an infinite amount of time for the chunk of matter, only for an outside observer!

'What about Hawking radiation? Won't the black hole evaporate before you get there?'

Take a look at our Black Hole FAQ thread.

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"All your bias are belong to us." Ara Pacis
"A witty saying proves nothing." Voltaire

I think you're absolutely right.

I think you are, though I can't venture an explanation. Light speed is definitely constant in a vacuum, but near the event horizon space itself is curved...

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"All your bias are belong to us." Ara Pacis
"A witty saying proves nothing." Voltaire

OK, thanks DA for linking to that explanation. So we see how to get around the Hawking radiation problem, it's kind of a technicality (albeit an important one). But this proves that Astrowannabe's question was indeed well founded (as I said before, I did not prescribe to the 'general opinion'
Astrowannabe referred to that the problem with his question was all an illusion). It is true that from our perspective on Earth, black holes never actually form. There are no black holes for us, expect any that were here 'from the beginning'. However, there are things that act enough like black holes to make the distinction unimportant.

As you once wrote, if it quacks like one...

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"All your bias are belong to us." Ara Pacis
"A witty saying proves nothing." Voltaire

yup!

[He appears to have not crossed the event horizon as seen by the distant observer,]

Tim, if this is true...if nothing 'appears' to cross the event horizon, as seen from earth, then how do we 'see' black holes feeding? Or, do we actually see it? Or, is it just assumed that it must be?

I saw a link, where a radio experiment showed a black hole taken years apart, at a certain frequency, appeared to be 'feeding'.

__________________
RussT
________________________________
Everything is, as it should be, otherwise, it wouldn't be!

However, we ARE outside observers, so from OUR point of view no black hole even finished collapsing yet! As far as we are concerned, all the material that ever fell into any black hole, including the original star, is still hovering just outside event horizon.

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Fiction has to be plausible. Reality is under no such constraint.

We never see the black hole, we see the accretion disk-- material on the way to the event horizon. We could never see inside the event horizon anyway. But note that the gravity is contributed by all the gas that is near the event horizon, it doesn't matter if it's in the hole yet or not.

Thanks for the links, DA! That really cleared a few things up.

Apparently it appears that this:

Is not true. Just because we see him at spot A doesn't mean he's really there. Us seeing that image of him actually is an illusion. But if that's true, why is it that if he turns around and comes back to the rest of the universe, then the time dialation is no longer an illusion and becomes reality? Is it somehow due to climbing out of the gravity well?

So thanks to everyone that helped answer this!

An important thing to clarify is that any illusory effects due to the finite speed of light you can easily correct for. The interesting stuff of relativity is what is left after you so correct. That includes things like time slowing to a standstill near the event horizon, from the perspective of us on Earth.