Understanding Black Holes: Questions About Event Horizon

In summary: I don't think that's correct, do you have a reference? For example, I know that it is possible to model a black hole which forms and then evaporates due to Hawking radiation in a finite time--an outside observer will not see any object reach the horizon until the moment the hole evaporates completely (including the original material that formed the black hole in the first place, presumably), but from the perspective of the infalling observer, they do cross the event horizon in a finite time and there is a singularity inside. See the discussion http://cosmology.berkeley.edu/Education/BHfaq.html#q9. So, it seems plausible that the same sort of thing would be true of a black hole
  • #1
Wizardsblade
148
0
I was reading wiki's blckhole page and its diseription of what happens as you approach/enter the event horizone does not seem to make since to me. Spocificaly things like

"An infalling object takes a finite proper time (i.e. measured by its own clock) to fall past the event horizon. This in contrast with the infinite amount of time it takes for a distant observer to see the infalling object cross the horizon."

It seems to me that even though a distant observer would say the falling man's watch is really slow, the falling man would still be moving at a really fast speed across the event horizon.

Even the discription of inside the event horizon seems off to me. Is this what is generaly accepted and if so is there somewhere I can read on why we believe these things to me true?
 
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  • #2
Keep in mind that the distant observer cannot see inside the black hole. The observer sees no light coming out from inside the horizon. As the victim falls closer to the horizon, light coming from him is increasingly red-shifted to the observer, and the victim's clock appears to run slower and slower (relative to the observer), up to the point where he hits the horizon, at which point his clock appears to have stopped (though the observer wouldn't see this as by then the light would have been infinitely red shifted, i.e. invisible).

The observer, of course, feels nothing strange as he crosses the horizon. He does see that he's accelerating towards the centre (and possibly feeling the effects of tidal forces).
 
  • #3
DopplerDog said:
The observer, of course, feels nothing strange as he crosses the horizon. He does see that he's accelerating towards the centre (and possibly feeling the effects of tidal forces).

That should be "the victim... feels nothing strange". I placed the observer far away from the horizon, and the victim traveling towards it.
 
  • #4
Wizardsblade said:
"An infalling object takes a finite proper time (i.e. measured by its own clock) to fall past the event horizon. This in contrast with the infinite amount of time it takes for a distant observer to see the infalling object cross the horizon."
There is no contradiction since the model assumes an asymptotically flat space at infinity.
 
  • #5
MeJennifer said:
There is no contradiction since the model assumes an asymptotically flat space at infinity.
I don't think this has anything to do with it--they aren't talking about the time needed to fall in from infinity, but just the time needed to fall in from some finite radius outside the event horizon, which would still appear infinite to the outside observer if he could see light of arbitrarily large wavelengths and if light were emitted continuously rather than in a discrete series of photons (see the discussion here). Pretty sure the same would be true for a black hole in a non-asymptotically flat universe, such as a closed universe with positive curvature.
 
  • #6
JesseM said:
I don't think this has anything to do with it--they aren't talking about the time needed to fall in from infinity, but just the time needed to fall in from some finite radius outside the event horizon, which would still appear infinite to the outside observer if he could see light of arbitrarily large wavelengths and if light were emitted continuously rather than in a discrete series of photons (see the discussion here). Pretty sure the same would be true for a black hole in a non-asymptotically flat universe, such as a closed universe with positive curvature.
A closed universe cannot possibly have black holes.
 
  • #7
MeJennifer said:
A closed universe cannot possibly have black holes.

I have heard this elsewhere. Does that come from the definition of a black hole?
 
  • #8
kev said:
I have heard this elsewhere. Does that come from the definition of a black hole?
There would simply be not enough time for an event horizon to completely form in a closed universe.
 
  • #9
MeJennifer said:
There would simply be not enough time for an event horizon to completely form in a closed universe.
I don't think that's correct, do you have a reference? For example, I know that it is possible to model a black hole which forms and then evaporates due to Hawking radiation in a finite time--an outside observer will not see any object reach the horizon until the moment the hole evaporates completely (including the original material that formed the black hole in the first place, presumably), but from the perspective of the infalling observer, they do cross the event horizon in a finite time and there is a singularity inside. See the discussion http://cosmology.berkeley.edu/Education/BHfaq.html#q9. So, it seems plausible that the same sort of thing would be true of a black hole in a closed universe, outside observers couldn't see anything cross the horizon at any moment before the black hole was destroyed in the big crunch, but infalling observers could cross it in a finite time.
 
  • #11
MeJennifer said:
There would simply be not enough time for an event horizon to completely form in a closed universe.

Why? Why can't a supermassive star have the time to go supernova and produces a black hole in a closed universe??
 
  • #12
MeJennifer said:
In this respect you might want to read Tipler's article in Nature.

http://www.nature.com/nature/journal/v270/n5637/pdf/270500a0.pdf
The full article isn't available unless you're a subscriber, but the abstract doesn't appear to say that event horizons can't form in closed universes, in fact it says that by defining a black hole in terms of trapped surfaces one can talk about black holes in closed universes:
I shall extend the concept of 'black hole' to arbitrary stably causal spacetimes by essentially defining a black hole to be that object which contains all the 'small' trapped surfaces. As for most astrophysical applications black hole surfaces are located approximately by the outermost trapped surface boundary, this new definition allows results which depend only on the local behaviour of black holes in asymptotically flat spacetimes to be extended (approximately) to closed universes.
It does say that other results such as the black hole area theorem (that black holes never decrease their cross-sectional area, ignoring Hawking radiation) cannot be extended to closed universes, though.

Also, googling "trapped surface" and "black hole" and "closed universe" I came across this google book search result which says:
Condition (4) is closely connected, as we have already mentioned, with the existence of a black hole. The Penrose-Hawking theorem guarantees that a singularity arises also in the case when a trapped surface is generated, say, in a closed universe.
 
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  • #13
MeJennifer said:
There would simply be not enough time for an event horizon to completely form in a closed universe.

I'd have preferred an argument based upon the second law of thermodynamics.

Does a black hole do work while concentrating energy within an arbitrary closed system?

Regards,

Bill
 
  • #14
I do not think it is worth arguing about it, if you think that closed spacetimes can contain black holes then so be it.
 
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  • #15
Antenna Guy said:
I'd have preferred an argument based upon the second law of thermodynamics.
Yes that works as well.
 
  • #16
MeJennifer said:
I do not think it is worth arguing about it, if you think that closed spacetimes can contain black holes then so be it.
I doubt either one of us is qualified to make independent judgments on this issue, so the question here is what professional physicists think about it. The quotes I posted seem to say that black holes can indeed form in closed universes--do you disagree with my understanding of what the quotes are saying, or are you trying to say that you think these physicists are wrong? Presumably their statements are based on study of mathematical models in GR, not qualitative arguments.
 
  • #17
Antenna Guy said:
Does a black hole do work while concentrating energy within an arbitrary closed system?
The behavior of a black hole is thought to increase entropy in accord with the 2nd law of thermodynamics, if that's what you're talking about--see black hole thermodynamics.
 
  • #18
JesseM said:
The behavior of a black hole is thought to increase entropy in accord with the 2nd law of thermodynamics, if that's what you're talking about--see black hole thermodynamics.

Am I not reading correctly, or does the "second law of black hole mechanics" imply that an arbitrary closed surface (that does not grow with time) cannot be constructed about a black hole that gains energy?

Clearly, "a closed universe" is not equivalent to a black hole's event horizon.

Regards,

Bill
 
  • #19
Antenna Guy said:
Am I not reading correctly, or does the "second law of black hole mechanics" imply that an arbitrary closed surface (that does not grow with time) cannot be constructed about a black hole that gains energy?
Why do you think it says that? The second law concerns the area of the event horizon, it doesn't say anything about a larger surface around the black hole.
Antenna Guy said:
Clearly, "a closed universe" is not equivalent to a black hole's event horizon.
Who said they were equivalent? What would it even mean for them to be equivalent? I don't follow you at all.
 
  • #20
JesseM said:
Why do you think it says that? The second law concerns the area of the event horizon...

What does it say about the area of the event horizon?

Who said they were equivalent? What would it even mean for them to be equivalent? I don't follow you at all.

No offense, but I didn't claim that the wiki page supported my argument.

Regards,

Bill
 
  • #21
Antenna Guy said:
What does it say about the area of the event horizon?
It says the area of the event horizon always increases rather than decreasing, provided that something called the "weak energy condition" is satisfied (it is violated by Hawking radiation I think). It is believed that a black hole's entropy is proportional to its surface area, so this is thought to be a special case of the second law of thermodynamics. See this page for some more details.
Antenna Guy said:
No offense, but I didn't claim that the wiki page supported my argumentl
I wasn't talking about the wiki page, I was just saying that your statement 'Clearly, "a closed universe" is not equivalent to a black hole's event horizon' seems like a weird non sequitur to me, since I don't know of anyone (on this thread or elsewhere) who has suggested a closed universe is "equivalent" to a black hole's event horizon, or what that would even mean.
 
  • #22
JesseM said:
It is believed that a black hole's entropy is proportional to its surface area, so this is thought to be a special case of the second law of thermodynamics.

Let's say that the surface area of a black hole (loosely defined as it's event horizon) defines a dynamic (changing size with time) closed system in which the entropy of the system does not decrease. This is not a "special case of the second law of thermodynamics", it is a condition under which the entropy of a closed system containing a black hole does not violate the second law of thermodynamics.

Now consider an arbitrarily larger closed system that contains a random distribution of bodies of mass - including a black hole. As not-so-massive bodies within the control volume fall toward the black hole, the entropy of the *system* decreases as the distribution of energy (mass) becomes less random - violating the second law of thermodynamics.

I suppose one might argue that a closed universe of perpetually increasing volume/area might support the existence of localized decreased entropy... but, would such a universe be considered "closed" in the usual sense?

Regards,

Bill
 
  • #23
JesseM said:
The behavior of a black hole is thought to increase entropy in accord with the 2nd law of thermodynamics.

Penrose points out in "Road to Reality" how this presents a bit of a puzzle for cosmologists. On the one hand, the big bang must have occurred in a "thermalized" state, because the background cosmic radiation is more or less uniform. This means that the radiation must have been in thermal equilibrium: a high state of entropy.

On the other hand, matter finds itself in the highest state of entropy when it's in a black hole (which has an enourmous amount of entropy). Since matter in the early universe was NOT concentrated in black holes, the universe was, relatively speaking, in an incredibly low state of entropy as far as gravitation goes.

This would mean that at that point, the universe was thermally in a high state of entropy, but gravitationally it was in a ridiculously low state of entropy. The puzzle is why would there be a distinction between these degrees of freedom?

A second puzzle is the very nature of the 2nd law - which can be attributed to this puzzling low gravitational entropy. How did the universe find itself in such a ridiculously low entropy state to begin with?
 
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  • #24
Antenna Guy said:
Let's say that the surface area of a black hole (loosely defined as it's event horizon) defines a dynamic (changing size with time) closed system in which the entropy of the system does not decrease. This is not a "special case of the second law of thermodynamics", it is a condition under which the entropy of a closed system containing a black hole does not violate the second law of thermodynamics.

Now consider an arbitrarily larger closed system that contains a random distribution of bodies of mass - including a black hole. As not-so-massive bodies within the control volume fall toward the black hole, the entropy of the *system* decreases as the distribution of energy (mass) becomes less random - violating the second law of thermodynamics.
One of the main points of black hole thermodynamics is that if you take the area of the black hole as a measure of its entropy, then if you measure the total entropy of a closed system containing both the black hole and other stuff outside its event horizon, then the second law does hold because whenever matter/energy falls into the hole, any resulting decrease in the entropy of the system outside the black hole is compensated for by the black hole's size increasing because of the added mass, with its entropy increasing by an amount greater than or equal to the decrease outside.
Antenna Guy said:
I suppose one might argue that a closed universe of perpetually increasing volume/area might support the existence of localized decreased entropy... but, would such a universe be considered "closed" in the usual sense?
I think I might see the confusion here...do you understand that "closed" in the cosmological context of a "closed universe" means something completely different than "closed" in the thermodynamics sense of a "closed system"? In the cosmological sense I think it basically just means that the amount of space is finite, like the surface of a globe, so that if you go far enough in any direction you return to your place of origin.
 
  • #25
JesseM said:
One of the main points of black hole thermodynamics is that if you take the area of the black hole as a measure of its entropy, then if you measure the total entropy of a closed system containing both the black hole and other stuff outside its event horizon, then the second law does hold because whenever matter/energy falls into the hole, any resulting decrease in the entropy of the system outside the black hole is compensated for by the black hole's size increasing because of the added mass, with its entropy increasing by an amount greater than or equal to the decrease outside.

I think I might see the confusion here...do you understand that "closed" in the cosmological context of a "closed universe" means something completely different than "closed" in the thermodynamics sense of a "closed system"? In the cosmological sense I think it basically just means that the amount of space is finite, like the surface of a globe, so that if you go far enough in any direction you return to your place of origin.

I think the confusion comes from the terminology of thermodynamics. A closed system in thermodymanics does not follow the casual meaning of "closed" and is a system with a boundary which is energy and work may be exchanged with its environment but no matter is allowed to cross the boundary. Talking about the total entropy of a closed system containing both the black hole and other stuff outside its event horizon is meaningless if the amount of energy or work crossing the closed boundary is not defined. If it was meant to imply a closed system where nothing crosses the boundary then the formal definition of that type of system in thermodynamics is a insulated system. I think the universe as a whole is probably as close as you are going to get to a perfect large scale insulated thermodynamic system unless of course it is suggested that matter or energy somehow escapes the universe.
 
  • #26
JesseM said:
I think I might see the confusion here...do you understand that "closed" in the cosmological context of a "closed universe" means something completely different than "closed" in the thermodynamics sense of a "closed system"? In the cosmological sense I think it basically just means that the amount of space is finite, like the surface of a globe, so that if you go far enough in any direction you return to your place of origin.

If we're speaking of thermodynamics, which of those meanings do you figure would be appropriate?

Regards,

Bill
 
  • #27
Antenna Guy said:
If we're speaking of thermodynamics, which of those meanings do you figure would be appropriate?
But you didn't just use the word "closed", you used the phrase "closed universe"--that phrase always refers to a cosmological context, if you want to use the word in a thermodynamic context you should just say something like "closed system". And I had forgotten about the distinction between "closed" and "isolated" in thermodynamics, but kev is correct, a closed system can actually exchange energy with the outside universe, if you want to refer to a system that exchanges neither matter or energy with the outside the phrase to use is isolated system. The second law of thermodyanamics says that the entropy in an isolated system will always tend to increase or remain constant, but the same isn't true for a closed system.
 
  • #28
JesseM said:
But you didn't just use the word "closed", you used the phrase "closed universe"--that phrase always refers to a cosmological context, if you want to use the word in a thermodynamic context you should just say something like "closed system".

All I can say at this point is that the "arbitrarily larger closed system" I referred to in post 22 could easily contain a finite universe. If a closed universe (in whatever context) is not finite, how can one call it closed? Is there some other esoteric context that I'm missing?

Regards,

Bill
 
  • #29
Antenna Guy said:
All I can say at this point is that the "arbitrarily larger closed system" I referred to in post 22 could easily contain a finite universe. If a closed universe (in whatever context) is not finite, how can one call it closed? Is there some other esoteric context that I'm missing?
A closed spacetime is always finite while an open spacetime is always infinite.
 
  • #30
Antenna Guy said:
All I can say at this point is that the "arbitrarily larger closed system" I referred to in post 22 could easily contain a finite universe. If a closed universe (in whatever context) is not finite, how can one call it closed? Is there some other esoteric context that I'm missing?
Again, in thermodynamics it is really isolated systems you should be talking about if you want to discuss the second law, not closed ones. But I suppose a finite universe might be considered a large isolated system. Anyway, as I said, there is no violation of the second law as long as you say that a black hole's entropy is defined by the area of its event horizon, since when matter or energy falls in the event horizon grows by an amount enough to offset any decrease in entropy in the region outside the event horizon. And I still don't understand why you said 'Clearly, "a closed universe" is not equivalent to a black hole's event horizon'--has anyone said they should be equivalent, or is there any argument to suggest they would? Among other things the event horizon is 2-dimensional while a finite universe is 3-dimensional.
 
  • #31
JesseM said:
Again, in thermodynamics it is really isolated systems you should be talking about if you want to discuss the second law, not closed ones. ... Anyway, as I said, there is no violation of the second law as long as you say that a black hole's entropy is defined by the area of its event horizon, since when matter or energy falls in the event horizon grows by an amount enough to offset any decrease in entropy in the region outside the event horizon.

Are you sure that's what you want to say?

Regards,

Bill
 
  • #32
JesseM said:
Again, in thermodynamics it is really isolated systems you should be talking about if you want to discuss the second law, not closed ones. ... Anyway, as I said, there is no violation of the second law as long as you say that a black hole's entropy is defined by the area of its event horizon, since when matter or energy falls in the event horizon grows by an amount enough to offset any decrease in entropy in the region outside the event horizon.
Antenna Guy said:
Are you sure that's what you want to say?
Yes. Weren't we discussing a larger isolated system that contains both a black hole and some matter/energy outside it? That's what you seemed to be talking about in the second paragraph of post #22 (which begins 'Now consider an arbitrarily larger closed system that contains a random distribution of bodies of mass - including a black hole'), and that's what I was responding to. So, for the larger system to qualify as "isolated" it must be true that no matter/energy is crossing the boundary of the larger system (say, a giant box containing a black hole and some other stuff), but matter/energy can certainly cross the event horizon.
 
  • #33
JesseM said:
Yes.

Consider how the entropy of a black hole changes within the context of the first bold.

Is a black hole an "isolated system"?

Regards,

Bill
 
  • #34
Antenna Guy said:
Is a black hole an "isolated system"?
No, it is not.
 
  • #35
Antenna Guy said:
Consider how the entropy of a black hole changes within the context of the first bold.

Is a black hole an "isolated system"?
On its own? Not if any matter/energy crosses the event horizon, by definition.
 

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