Can Energy Really Exist on the Surface of a Black Hole?

[Rlam90]

I don't like the idea of anything crossing the event horizon of a black hole from any observer's view point. The closer something gets to the event horizon, it either appears to slow down, or the event horizon appears to stretch and move further away. How can anything cross it?

For this reason, i like the idea that all the energy in a black hole is concentrated in a shell on the surface. This, in turn, leads me to believe that all matter is energy condensed around localized coordinates. Unfortunately, I don't have any citations or math to back me up. I'm curious how much legitimacy there is to these thoughts.

 

[Rlam90]

Also, it seems like this would imply that there is no point where escape is impossible, as nothing crosses the event horizon. This would make it easier to fit black holes into accepted theories of thermodynamics, as information never really becomes inaccessible, just highly fixed.

Now, about their formation. Theoretically, the original "event horizon" would form as a collapsing star compresses two bundles of energy into a small area. Actually, this is likely to happen in many locations near simultaneously. As additional matter approaches these bundles of gravitational energy, the event horizons would stretch and merge, coalescing into the celestial bodies we can "see".

Now a question: suppose an object passes between two of the forming event horizons, would its timeframe be slowed by both gravitational fields or would they cancel out? I am assuming the former, as time dilation is independent of spatial velocity direction.

 

[DaveC426913]

I don't like the idea of anything crossing the event horizon of a black hole from any observer's view point. The closer something gets to the event horizon, it either appears to slow down, or the event horizon appears to stretch and move further away. How can anything cross it?

You might like it more if you read up on it a little.

It is only from the point of a distant observer that an object doesn't appear to cross the EH. That's because of the fallible nature of observations by light.

An observer falling into an EH will cross the EH with no untoward effects - afterall, the EH is not a thing at all, nothing actually happens there. It is a derived point at a radius, nearer than which light cannot escape. That means nothing to an infalling observer, and they neither know nor experience anything about it. They could calculate when they'd crossed the EH, just like you could calculate when a trip to the cottage was exactly half over. But nothing changes at the halfway point to the cottage - there's no physical significance to this point.

And after all that, rest assured, the infalling observer will proceed to the singularity in an extremely finite time.

 

[Rlam90]

So what exactly is time dilation? Doesn't gravity slow each particle's 'clock' as they approach the source? I have been under the impression that as a particle's movement through space increases, its world-line is skewed so that it takes a path almost perpendicular to the time axis. I noticed that the lorentz factor is just a form of pythagoras's theorem stating the hypotenuse as the speed of light and spatial velocity as one side ofthe triangle. I figured spacetime velocity was constant.

Do you have any recommended reading for me?

 

[Matterwave]

The time dilation due to gravity is always an Observer 1 observering observer 2 (in a stronger gravitational field) to have time dilation. To any observer observing his own time, his time MUST click by normally (he cannot, by definition, notice the "time dilation" on himself).

You can see this easily if you think about Einstein's Equivalence principle. No local experiment done in freefall can distinguish whether you are in a gravitational field or not (e.g. you can't tell the difference between just floating out in space, and freefalling in some gravitational field). This means, for the observer free-falling into the black hole, he can't actually tell if he fell through the EH or not at all (assuming he doesn't get "spaghettified"). You can't actually locally measure the curvature of spacetime. You can only measure curvature through tidal forces (this is what causes "spaghettification").

This is particularly apparent if you transform to Eddington-Finklestein coordinates or Kruskal-Szekeres coordinates (pardon the spelling...), where no singularity appears at the Event Horizon. For this reason, we call the event horizon a "coordinate singularity", it's not a real physical singularity.

 

[Rlam90]

But relative to the particles ahead of the observer near an event horizon, the distance between the two would be streched. And this would apply to each subsequent particle closer to the horizon. So from any real viewpoint, nothing ever reaches the boundary. Is this different than general relativity? I guess this thinking comes from the idea that space is not a coordinate plane but a measurement of the 'time' it would take a particle to travel to any other particle.

Hope I'm making sense.

 

[Rlam90]

I'm sorry, it's late. The measurement i mentioned was energy, not time.

 

[Dale]

But relative to the particles ahead of the observer near an event horizon, the distance between the two would be streched. And this would apply to each subsequent particle closer to the horizon. So from any real viewpoint, nothing ever reaches the boundary.

This depends on the mass of the black hole. For an arbitrarily large black hole the tidal effects become arbitrarily small. So you could cross the event horizon of a super massive black hole without noticing any stretching at all.

 

[DaveC426913]

But relative to the particles ahead of the observer near an event horizon, the distance between the two would be streched. And this would apply to each subsequent particle closer to the horizon. So from any real viewpoint, nothing ever reaches the boundary. Is this different than general relativity? I guess this thinking comes from the idea that space is not a coordinate plane but a measurement of the 'time' it would take a particle to travel to any other particle.

Hope I'm making sense.

Again, observation of other objects within the black hole's influence does not change one's own path into the black itself.

 

[pervect]

Note that an accelerated observer has an event horizon which is mathematically very similar to the event horizon of a black hole.

It is quite possible to imagine the Earth falling into the Rindler horizon of such an accelerating observer.

The accelerating observer will never see the Earth cross the horizon, but the people on the Earth will see it happen at some specific date, say New Years day in 2012.

The accelerated observer watching the Earth fall into the horizon will never see any event beyond this date, i.e. he will only see events before New Years day 2012.

However, it would be quite a mistake for the accelerated observer to conclude from this that "the world ends in 2012", or that "the Earth never falls beyond the horizon".

It seems to me that this is just the mistake you are making, though.

 

[mrspeedybob]

Note that an accelerated observer has an event horizon which is mathematically very similar to the event horizon of a black hole.

It is quite possible to imagine the Earth falling into the Rindler horizon of such an accelerating observer.

The accelerating observer will never see the Earth cross the horizon, but the people on the Earth will see it happen at some specific date, say New Years day in 2012.

The accelerated observer watching the Earth fall into the horizon will never see any event beyond this date, i.e. he will only see events before New Years day 2012.

However, it would be quite a mistake for the accelerated observer to conclude from this that "the world ends in 2012", or that "the Earth never falls beyond the horizon".

It seems to me that this is just the mistake you are making, though.

From the Earth's perspective it is a mistake, from the accelerated observers perspective it is not. Reletivity does not describe illusions, it describes things that are actually different for 2 observers. You can't say 1 observer is right and the other is wrong.

The same applies to a black holes event horizon.

 

[Constantin]

It is only from the point of a distant observer that an object doesn't appear to cross the EH. That's because of the fallible nature of observations by light.

It doesn't have to do with "the fallible nature of observations by light". It's simply not considered possible to observe beyond the event horizon.
It also doesn't have to be "from the point of a distant observer". Any observer outside the event horizon will do just fine, no matter how close. That means all observers that exist for us.

 

[Constantin]

I don't like the idea of anything crossing the event horizon of a black hole from any observer's view point. The closer something gets to the event horizon, it either appears to slow down, or the event horizon appears to stretch and move further away. How can anything cross it?

That sounds perfectly valid from the point of view of any observer outside the event horizon (which means all observers that exist for us).

If you keep your ideas about black holes simple, and only consider what an outside observer would be able to see, you'll be spared a lot of headaches.

 

[pervect]

From the Earth's perspective it is a mistake, from the accelerated observers perspective it is not. Reletivity does not describe illusions, it describes things that are actually different for 2 observers. You can't say 1 observer is right and the other is wrong.

The same applies to a black holes event horizon.

In my example, it is a false statement to say that no observer observes events after 2012. So if you are making statements about an observer-independent reality, it is false to say that "you never cross the black horizon", for the very reason that statements that are true and observer independent must be true for all observers.

("Statements about observer independent facts" is my operational definition of "statements about reality" by the way).

If you qualify the statements, such as "The external observer never sees the object cross the black hole", or "Using the particular notion of simultaneity used by static observers, the time of the event that's simultaneous with the horizon crossing approaches infinity", you'll be OK.

Note that the notion of simultaneity used by moving observers is different from the notion of simultaneity used by static observers. If this isn't obvious, perhaps a different discussion on the "relativity of simultaneity" is in order.

So saying "it never happens" is false, because for some observers it does happen.

 

[DaveC426913]

It doesn't have to do with "the fallible nature of observations by light".

Sorry, I was oversimplifying. Two observers in relativity will not agree in the same sequence of events.

This gets worse the farther apart they are. However, if one spaceship followed immediately behind another into the BH, the apparent discrepancy in events would be correspondingly reduced.

It's simply not considered possible to observe beyond the event horizon.
It also doesn't have to be "from the point of a distant observer". Any observer outside the event horizon will do just fine, no matter how close. That means all observers that exist for us.

The OP seems to be seeing a discontinuity between what is observed from outside the BH and what occurs at the EH. The discontinuity will resolve itself to the observer who gets closer and closer to the object about to enter the EH.

To point where, if the observer is pulls up parallel to the initial object (i.e. distance reduced to zero) as it enters the EH, they will not observe the object experiencing this halting at the EH.

 

[zonde]

I don't like the idea of anything crossing the event horizon of a black hole from any observer's view point. The closer something gets to the event horizon, it either appears to slow down, or the event horizon appears to stretch and move further away. How can anything cross it?

For this reason, i like the idea that all the energy in a black hole is concentrated in a shell on the surface. This, in turn, leads me to believe that all matter is energy condensed around localized coordinates. Unfortunately, I don't have any citations or math to back me up. I'm curious how much legitimacy there is to these thoughts.

If you don't buy the idea that anything can cross event horizon then there is no reason to believe that there are object that we can describe as black holes.
So your idea about "shell black holes" seems contradictory.

 

[Constantin]

If you don't buy the idea that anything can cross event horizon then there is no reason to believe that there are object that we can describe as black holes.

I see no logic in what you're saying.
You can consider that nothing passes through the event horizon, and still have reason to believe that there are black holes.

The fact that nothing passes through the event horizon can be a simplification by considering only what an observer can see, and not bothering with what happens but we can't see.
The existence of black holes is not about personal belief, as many were discovered. In the case of Sagittarius A, situated in the center of our galaxy, the evidence is very strong for it being a supermassive black hole.

 

[zonde]

I see no logic in what you're saying.
You can consider that nothing passes through the event horizon, and still have reason to believe that there are black holes.

The logic is simple - if nothing passes event horizon of some hypothetical seed black hole then it can't grow it's mass and expand it's EH.

The fact that nothing passes through the event horizon can be a simplification by considering only what an observer can see, and not bothering with what happens but we can't see.
The existence of black holes is not about personal belief, as many were discovered. In the case of Sagittarius A, situated in the center of our galaxy, the evidence is very strong for it being a supermassive black hole.

About what kind of evidence you are talking? There is very massive object at the center of Milky Way. And that's about it.
What specific evidence we can have to claim that this very massive object has something like event horizon?

 

[Constantin]

The logic is simple - if nothing passes event horizon of some hypothetical seed black hole then it can't grow it's mass and expand it's EH.

It would probably grow just the same way no matter what the interior looks like. Or whether it does or doesn't have an interior.

About what kind of evidence you are talking? There is very massive object at the center of Milky Way. And that's about it.
What specific evidence we can have to claim that this very massive object has something like event horizon?

Quoted from:
http://en.wikipedia.org/wiki/Sagittarius_A*

"the object's mass can be estimated as 4.1 million solar masses."
"recent observations[16] indicate that the radius is no more than 6.25 light-hours, about the diameter of Uranus' orbit"
"The only widely hypothesized type of object which can contain 4.1 million solar masses in a volume that small is a black hole."

"While, strictly speaking, there are other mass configurations that would explain the measured mass and size, such an arrangement would collapse into a single supermassive black hole on a timescale much shorter than the life of the Milky Way."

----
Another case of a confirmed black hole is Cygnus X-1 .
Link:
http://en.wikipedia.org/wiki/Cygnus_X-1

There's an interesting paragraph at the end of the wikipedia page with a wager between physicists Stephen Hawking and Kip Thorne on this subject.

 

[mrspeedybob]

An object can look like a black hole without having an event horizon.
As the object collapses all processes that produce light are time dilated to very nearly stopped. Any light that is produced is red-shifted to oblivion. Even the process of collapse itself must slow to a virtual standstill. All this of course from an outside observers standpoint.

An infilling observer sees the whole thing crushed to a singularity but if he looks behind him he sees the universe grow infinitely old while it's happening.

Since we are outside observers and since the universe is not infinitely old then it seems to me that objects with event horizons cannot exist in our universe.

 

[Constantin]

Since we are outside observers and since the universe is not infinitely old then it seems to me that objects with event horizons cannot exist in our universe.

The event horizons themselves however do exist. The Observable Universe itself has such an event horizon.
Actually any event horizon is a boundary of the Observable Universe. If we can't observe what's beyond it, then whatever is "beyond" can't be part of the OU, right ?

"In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer."

 

[skeptic2]

I think some of you are forgetting that not only is time infinitely dilated at the horizon but radial distance is also infinitely contracted at the horizon allowing an infinite amount of matter to be packed into that last millimeter above the horizon. To the matter in that last mm, it isn't squeezed at all, in fact both the matter falling in ahead of it and the matter falling in behind it is moving farther away. So the matter just above its own EH sees an EH below it based on how much matter has fallen in before it. The matter below it always sees a smaller EH which it cannot cross. As matter falls in behind, it also sees an EH ahead of it which it can never cross.

So the following two quotes are not necessarily true. The EH can grow even if none of the matter ever crosses its own EH. An object can contain a huge mass in a small volume without that mass being inside the EH. Furthermore, once matter passes the EH, how could the gravity of that matter be felt outside the EH without violating causality?

The logic is simple - if nothing passes event horizon of some hypothetical seed black hole then it can't grow it's mass and expand it's EH.

"The only widely hypothesized type of object which can contain 4.1 million solar masses in a volume that small is a black hole."

"While, strictly speaking, there are other mass configurations that would explain the measured mass and size, such an arrangement would collapse into a single supermassive black hole on a timescale much shorter than the life of the Milky Way."

There's an interesting paragraph at the end of the wikipedia page with a wager between physicists Stephen Hawking and Kip Thorne on this subject.

I take issue with the idea in the following quote that an infalling observer will see the universe grow infinitely old. Just as the observer will see matter falling in behind him lag farther and farther behind, he will see light from that matter red shifted which indicates he will see the universe aging more slowly, not more rapidly.

An infilling observer sees the whole thing crushed to a singularity but if he looks behind him he sees the universe grow infinitely old while it's happening.

Since we are outside observers and since the universe is not infinitely old then it seems to me that objects with event horizons cannot exist in our universe.

 

[DaveC426913]

I take issue with the idea in the following quote that an infalling observer will see the universe grow infinitely old. Just as the observer will see matter falling in behind him lag farther and farther behind, he will see light from that matter red shifted which indicates he will see the universe aging more slowly, not more rapidly.

No, the infalling light will be blue-shifted, not red-shifted. corresponding to an increase in the passage of time.

 

[skeptic2]

It will be blue shifted for a stationary or hovering observer, but for a free falling observer it will be red shifted. It will be red shifted for the same reason that if you drop two objects, one right after the other, to either object the other will appear to move away from it.

 

[PeterDonis]

I think some of you are forgetting that not only is time infinitely dilated at the horizon but radial distance is also infinitely contracted at the horizon allowing an infinite amount of matter to be packed into that last millimeter above the horizon.

This is a common misconception, but it's not correct. The proper distance to the horizon from any radial coordinate above the horizon is finite. It is true that, as r -> 2M, the metric coefficient g_rr in Schwarzschild coordinates, which in some sense denotes "radial distance per increment of radial coordinate r", goes to infinity. But to compute the actual proper distance to the horizon, you have to compute the integral

ds = \int_{2M}^{R} \sqrt{g_{rr}} dr

where r = 2M is the horizon and R is the radial coordinate whose "distance to the horizon" you are interested in. Substituting from the metric, we get

ds = \int_{2M}^{R} \frac{1}{\sqrt{1 - \frac{2M}{r}}} dr = \int_{2M}^{R} \sqrt{\frac{r}{r - 2M}} dr

This integrates to a finite value, as you can see by looking up its general form in a table of integrals.

 

[skeptic2]

I appreciate your response Peter but I am not familiar with some of your notation. Is g_rr the contracted radius or the ratio between the contracted radius and the circumference (at the same point) divided by 2 pi.

 

[PeterDonis]

I appreciate your response Peter but I am not familiar with some of your notation. Is g_rr the contracted radius or the ratio between the contracted radius and the circumference (at the same point) divided by 2 pi.

g_rr is the metric coefficient of dr^2 in the line element. The general form of a line element is

ds^{2} = g_{ab} dx^{a} dx^{b}

where g_ab is the metric, viewed as a matrix of coefficients for coordinate indices a and b, and a and b run from 0 to 3. In most commonly used coordinate charts, x^0 is the "time" coordinate and x^1, x^2, x^3 are the "space" coordinates; but there are charts where things are not so simple (though we don't need to discuss them for this particular topic). Also, I have used the Einstein summation convention, where repeated indexes are summed over, so the above equation expands out to:

ds^{2} = \sum_{a, b = 0, 1, 2, 3} g_{ab} dx^{a} dx^{b}

For the spacetime outside a black hole, the line element looks like this in Schwarzschild coordinates, where the radial coordinate r is the circumference of a circle centered on the black hole at r, divided by 2 pi:

ds^{2} = - \left(1 - \frac{2M}{r} \right) dt^{2} + \frac{1}{1 - \frac{2M}{r}} dr^{2} + r^{2} d\Omega^{2}

where M is the mass of the black hole and d\Omega^{2} is the standard angular measure on a 2-sphere. (I am using units where G = c = 1, as is common in GR.) From this expression you can read off g_rr as the coefficient in the second term on the RHS.

This is all standard notation in GR and it's worth taking some time to become familiar with it if you aren't already.

 

[Passionflower]

I think some of you are forgetting that not only is time infinitely dilated at the horizon but radial distance is also infinitely contracted at the horizon allowing an infinite amount of matter to be packed into that last millimeter above the horizon.

No that is incorrect, it is true that you can pack more than one would expect if the volume would have been Euclidean but it is not that much more.

We can easily calculate this for a given Schwarzschild radius. For instance in the case the Schwarzschild radius is 1 the volume between the EH and a shell one millimeter above it for an observer at infinity is about: 0.00864134 versus 0.00000314 for if the space was Euclidean. So it is really nothing dramatic. For larger Schwarzschild radii it is virtually nonexistent.

However for a static observer near the event horizon radial distance, and thus volume as well, does increase without bound.

 

[mrspeedybob]

The event horizons themselves however do exist. The Observable Universe itself has such an event horizon.
Actually any event horizon is a boundary of the Observable Universe. If we can't observe what's beyond it, then whatever is "beyond" can't be part of the OU, right ?

"In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer."

There are 2 examples I can think of of possible event horizons...

A collapsing star, for reasons I already stated earlier will never collapse to the point of having an event horizon. An event that happens within the star will be extremely time dilated but not absolutely frozen in time. Light from that event will be extremely red shifted, but still can escape. If you had equipment that could make sense of light with a trillion light-year wavelength and time to wait for it you could observe the event.

As for the universe, we can see all the way back to the surface of last scattering. This is simply an opaque plasma and is no more of an event horizon then an ordinary opaque wall. If we could see past this by detecting some sort of non EM radiation we would simply see earlier times, perhaps even back to BB. I don't think the universe has an event horizon due to super-luminal expansion. Some day it may, but not yet.

 

[Q-reeus]

Originally Posted by skeptic2:
"I think some of you are forgetting that not only is time infinitely dilated at the horizon but radial distance is also infinitely contracted at the horizon allowing an infinite amount of matter to be packed into that last millimeter above the horizon."

No that is incorrect, it is true that you can pack more than one would expect if the volume would have been Euclidean but it is not that much more.

We can easily calculate this for a given Schwarzschild radius. For instance in the case the Schwarzschild radius is 1 the volume between the EH and a shell one millimeter above it for an observer at infinity is about: 0.00864134 versus 0.00000314 for if the space was Euclidean. So it is really nothing dramatic. For larger Schwarzschild radii it is virtually nonexistent.

Nothing much at all? Taking out my pocket calculator, I divide 0.00864134 by 0.00000314 and obtain 2752.02 - the ratio of volumes. [More precisely - I presume what we mean by volume here is the differential volume between two spherical surfaces having radii between r and r+dr, at 1mm above the 'EH'. Otherwise one runs into even greater absurdities. But see later re defining r] Which would have been unity in Euclidean measure. And try 0.1mm, 0.01mm, etc - trend is towards infinity as we all well know. And btw since I was taken to task in another thread for assuming radial distance can have some kind of 'normal' meaning in SC's, what and how do you define 1mm radial distance here, given the circular nature of defining such things? Can you logically escape the '(differential volume)/(differential surface area)' bind?

However for a static observer near the event horizon radial distance, and thus volume as well, does increase without bound.

And this is not a contradiction of the earlier remarks 'but it is not that much more.' ...'So it is really nothing dramatic.'?