Black Hole Radiation: Questions Clarified

[arlesterc]

A couple of points I need clarification on.

Objects outside of the event horizon feel the pull of the black hole - so the closer the object is to the event horizon but still outside of it the more pull the object feels to be sucked into the event horizon? Is that the correct view?

As far as virtual pair production that leads to Hawking radiation. Does it take place on the event horizon or just outside of it? In either case assuming one of the pair gets sucked into the black hole and the other doesn't, I am not following how energy is lost. So assuming we are talking about virtual photons - one virtual photon goes into the black hole /crosses the event horizon - maybe it was right on the horizon to start with - and the other dashes off. How does this cause the black hole to lose anything? It seems to me it gained a photon and the one that dashed away was never part of the black hole to begin with. So it seems it would look like the black hole has more energy/mass than it began with after such an event - one virtual photon to be exact. How does the black hole provide energy/mass to the photon that was never inside of it to the point the black hole loses energy/mass? I guess the deeper mystery to me is how energy is lost by gravity being just gravity? If you have a huge mass exerting gravity the concept of 'radiation' applied to it would seem to be equivalent to saying that if another much smaller object is brought close to it and starts feeling the force of gravity some of the mass/energy of the large object is lost because there is something close by to feel its gravity - if there was no such nearby object then 'gravity' would not 'lose energy'. Any assistance in clearing this up would be greatly appreciated.

 

[phinds]

A couple of points I need clarification on.

Objects outside of the event horizon feel the pull of the black hole - so the closer the object is to the event horizon but still outside of it the more pull the object feels to be sucked into the event horizon? Is that the correct view?

Technically yes, but you're overthinking it. As you pass from say a few miles outside the EH of a supermassive BH to a few miles inside, you'll observer practically no change in anything.

As far as virtual pair production that leads to Hawking radiation ...

The "virtual pair production" is a hueristic that Hawking came up with because he could not figure out any other way to say in English something that really can only be said with math.

I suggest a forum search. This topic has been beaten to death HUNDREDS of times here on PF.

 

[arlesterc]

I have done a forum search - did not clarify. I am not sure why your first assumption is that I haven't.

+++++++
As far as: "Technically yes, but you're overthinking it. As you pass from say a few miles outside the EH of a supermassive BH to a few miles inside, you'll observer practically no change in anything."

For one thing as far as I understand the two objects will no longer be able to contact each other. Seems to be a big difference.
++++++++
As far as "The "virtual pair production" is a hueristic that Hawking came up with because he could not figure out any other way to say in English something that really can only be said with math."

There are a lot of things that can be said with math better than any other way. However that doesn't mean they can't be approximated without math or math that has been simplified.. I see folks like Susskind and others of his reputation and standing using the virtual pair analogy to get their point across to a wider audience than those that know higher end mathematics. So I am not so sure there can't be a better explanation without math or some math that would help me.
If you posted just to let me know that you couldn't explain anything to me, thanks, you have accomplished your goal - I don't know anymore than when I started after reading your reply. However, I don't universalize your lack of ability to do that to all others on this forum. Perhaps somebody else will make an attempt and after they have I will have the feeling I understand a bit more. I won't be surprised by that but maybe you will. You are always free to post subsequently that it is an extreme trivialization and actually my impression that I know more is a conceit. Your call, your time.

 

[phinds]

For one thing as far as I understand the two objects will no longer be able to contact each other. Seems to be a big difference.

Sure, only one-way communication is possible, you are right about that. There are other differences as well. For one thing, once you cross the EH you can't get back out again but that doesn't make you feel any different at the time.

 

[Nugatory]

So assuming we are talking about virtual photons - one virtual photon goes into the black hole /crosses the event horizon - maybe it was right on the horizon to start with - and the other dashes off. How does this cause the black hole to lose anything? It seems to me it gained a photon and the one that dashed away was never part of the black hole to begin with.

One particle in the pair has negative mass/energy and the other has positive mass/energy. The one that ends up inside the black hole is always the negative-energy one while the positive-energy one escapes, so the mass/energy of the black hole is reduced by the interaction.

You might reasonably ask why it's always the positive energy particle that escapes to infinity, and the answer is that you've just run up against the limitations of the heuristic explanation. You will get some help from here and you can get the real thing from Hawking himself here.

 

[roger painter]

Technically yes, but you're overthinking it. As you pass from say a few miles outside the EH of a supermassive BH to a few miles inside, you'll observer practically no change in anything.

The "virtual pair production" is a hueristic that Hawking came up with because he could not figure out any other way to say in English something that really can only be said with math.

I suggest a forum search. This topic has been beaten to death HUNDREDS of times here on PF.

hueristic

The prevailing opinion seems to be that a black hole’s matter is concentrated at its center as something that has near infinite density. Anything passing beyond the event horizon is thought to be accelerated to the massive center. Black holes can be overfed and observed to “belch” gases (molecules with rest mass) traveling near light speed. The idea of massive particles with escape velocity near light speed is hard to get your mind around. The escaping gases could it seems be slung off of a region of super massive particles in a temporary orbit (maybe more analogous to the outer edge of a light vortex) and awaiting assimilation. As the BH feeds the radius of the orbit (EH)_with escape velocity near c would increase with the mass of the center of mass (center).

I’m attracted to this heuristic idea by the symmetry of the visualization of a spiral galaxy with a super massive black hole at its center. Inside the black hole, far removed from its massive center, the apparent gravitational field could (possibly?) be moderated by this scenario in such a way that massive nearby bodies (that eventually form) would be the predominant local contributors to gravitation. In this visualization and given time and distance dilatation (takes near an eternity in our time to travel to the center), is it possible that an observer inside the black hole would see a similar environment to ours. Something along these lines might be germane to white holes and

I’m trying to find opinions, papers books etc. that suggest a possible model of the relativistic mass of massive particles spiraling into the event horizon at near light speed and perhaps even a solution of the GT for something like or a least similar to this heuristic. I’m hoping that in the process of disproving the heuristic that something significant can be learned.

 

[phinds]

I’m hoping that in the process of disproving the heuristic that something significant can be learned.

You cannot "disprove" a heuristic since it's already known to be false.

 

[roger painter]

Are you referring to the definition of the word "heuristic" or do you mean that a hydrogen atom traveling at the speed of light relative to the center of the black hole has finite mass?

 

[PeterDonis]

Objects outside of the event horizon feel the pull of the black hole - so the closer the object is to the event horizon but still outside of it the more pull the object feels to be sucked into the event horizon?

As far as "gravitational pull", a black hole works the same as any other object with the same mass. (There is a caution here, though, that the Newtonian equations for "gravitational pull" are not quite correct, and they get more and more incorrect as you get closer to the horizon.)

As far as virtual pair production that leads to Hawking radiation.

That is a pop science heuristic picture which should be taken with a very large amount of salt. In particular, none of the questions you ask in the rest of your post actually make sense when you drop this heuristic picture and try to understand the actual physics. If all you want to know is how Hawking radiation carries energy away from a black hole, the best short answer is simply that any object that emits radiation loses energy, so a black hole that emits radiation loses energy, and hence loses mass. There is a quantum aspect involved with black holes, since a classical black hole cannot emit anything; but again, if all you want to know is how the quantum part makes that possible, the best short answer is simply that quantum fields violate the conditions of the classical theorems that tell us that black holes can't emit anything.

 

[PeterDonis]

The prevailing opinion seems to be that a black hole’s matter is concentrated at its center as something that has near infinite density.

No, that's not the prevailing opinion. A black hole is vacuum inside; there is no matter anywhere. The "mass" of a black hole is a property of is spacetime geometry; it's not due to a bunch of stuff being trapped inside.

Inside the black hole, far removed from its massive center, the apparent gravitational field could (possibly?) be moderated

No, it can't. Please review the PF rules on personal speculation.

(Btw, the concept of a "gravitational field" does not make sense inside a black hole's event horizon; so it's not just that what you suggest is not possible, it's that it's not even well-defined in the first place.)

 

[Teslascience]

No, that's not the prevailing opinion. A black hole is vacuum inside; there is no matter anywhere. The "mass" of a black hole is a property of is spacetime geometry; it's not due to a bunch of stuff being trapped inside.
No, it can't. Please review the PF rules on personal speculation.

(Btw, the concept of a "gravitational field" does not make sense inside a black hole's event horizon; so it's not just that what you suggest is not possible, it's that it's not even well-defined in the first place.)

Hi, I'm just little bit confused, I understand your comment:
"A black hole is vacuum inside; there is no matter anywhere. The "mass" of a black hole is a property of is spacetime geometry; it's not due to a bunch of stuff being trapped inside."
But can you explain or give a link for further reading about your second statement: "Btw, the concept of a "gravitational field" does not make sense inside a black hole's event horizon" because till that time I thought that gravitational field and spacetime geometry having a close relationship even in a singularity.

 

[PeterDonis]

till that time I thought that gravitational field and spacetime geometry having a close relationship

They do under circumstances where the concept of "gravitational field" makes sense. That is the case in the region outside a black hole's horizon, but not inside the horizon. Outside the horizon, spacetime is static--you can find observers (the ones who are "hovering" at a constant altitude--radial coordinate--above the horizon) who see an unchanging spacetime geometry in their vicinity. So the worldlines of such observers can mark "points in space" that can be used to define the concept of a "gravitational potential"--potential energy due to gravity that depends on position--and the gradient of this potential is the gravitational field.

Inside the horizon, there are no such observers; it's impossible to "hover" at a constant radial coordinate. All observers must fall inward, to smaller and smaller radial coordinates, so they all see the spacetime geometry in their vicinity changing. In that kind of situation, there is no way to define "points in space" in the manner described above, no way to define the concept of a "gravitational potential", and no way to define the concept of a "gravitational field".

 

[JLowe]

No, that's not the prevailing opinion. A black hole is vacuum inside; there is no matter anywhere. The "mass" of a black hole is a property of is spacetime geometry; it's not due to a bunch of stuff being trapped inside.

Are you referring to the area inside the horizon, or the singularity itself? It is commonly explained that an observer can cross the horizon of a large enough black hole intact.

I realize no one really knows, I'm just trying to get an idea of what you're saying.

 

[PeterDonis]

Are you referring to the area inside the horizon

Yes.

It is commonly explained that an observer can cross the horizon of a large enough black hole intact.

Yes, but in such scenarios the observer's mass is assumed to be negligible compared to that of the hole. So he just falls through vacuum until he hits the singularity.

One could also consider a scenario where something large like a planet or a star falls into a black hole; in that scenario there would be a period where a significant portion of the hole's interior would be occupied by matter, as the planet or star's material got torn apart by the hole's tidal gravity and fell into the singularity. The end result would be a hole with a larger mass, which would once again be vacuum inside once the infall process was done.

 

[Teslascience]

They do under circumstances where the concept of "gravitational field" makes sense. That is the case in the region outside a black hole's horizon, but not inside the horizon. Outside the horizon, spacetime is static--you can find observers (the ones who are "hovering" at a constant altitude--radial coordinate--above the horizon) who see an unchanging spacetime geometry in their vicinity. So the worldlines of such observers can mark "points in space" that can be used to define the concept of a "gravitational potential"--potential energy due to gravity that depends on position--and the gradient of this potential is the gravitational field.

Inside the horizon, there are no such observers; it's impossible to "hover" at a constant radial coordinate. All observers must fall inward, to smaller and smaller radial coordinates, so they all see the spacetime geometry in their vicinity changing. In that kind of situation, there is no way to define "points in space" in the manner described above, no way to define the concept of a "gravitational potential", and no way to define the concept of a "gravitational field".

Thank you and I understand your explanation. I was curious because somewhere I read an other note which stated that because black holes occupying a measurable volume in spacetime that's why they must having inside the EH a gravitational or some other force of field too at least to the observer outside of it but I couldn't decide is this statement a speculation or mainstream science.

 

[PeterDonis]

somewhere I read

Where? Please give a reference.

 

[rootone]

a measurable volume

The black hole singularity does not have a measurable volume, which is why it is called a singularity.
The math leads to an object having zero volume and infinite density.
That is physically absurd, so we do know that inside the horizon of the black hole, there must be some physics going on that we don't know about.
The event horizon of a BH does have a size, but there is no actual surface there or anything else special

 

[Outhouse]

A black hole is vacuum inside; there is no matter anywhere

Couldn't we state the plausibility of no identifiable matter ?

Don't we know what the new size of a BH will be when one BH eats another BH, plus how much material is lost in the compilation of the 2 singularities?

My point, is it not wiser to state "there might not be matter anywhere" since we really don't know the math inside?

 

[PeterDonis]

is it not wiser to state "there might not be matter anywhere" since we really don't know the math inside?

We do know the math inside. The Schwarzschild solution is valid all the way to the singularity. Yes, it is assumed by most physicists that GR breaks down close enough to the singularity, but "close enough" here means roughly within a Planck length (or more appropriately a Planck time, since the singularity is really a moment of time). All the rest of the black hole interior is describable by the known math of GR.

Don't we know what the new size of a BH will be when one BH eats another BH, plus how much material is lost in the compilation of the 2 singularities?

There is no "material lost" when black holes merge. The mass of the merged hole might be less than the sum of the masses of the original holes (if the merged hole is rotating rapidly), but that mass does not "escape" as material. It is radiated away as gravitational waves, which are "made of" spacetime curvature and contain no material (no stress-energy).

 

[jbriggs444]

For one thing as far as I understand the two objects will no longer be able to contact each other. Seems to be a big difference.

As long as both are free-falling into the hole on a radially inward trajectory and are sufficiently close to one another, they can contact each other just fine. The event horizon does not prevent that.

True, an outbound message cannot pass through the event horizon. But a free-faller outside the horizon will fall through and can then receive the message.

 

[Outhouse]

There is no "material lost" when black holes merge.

Does that take into account the Final parsec problem?

Yes, it is assumed by most physicists that GR breaks down close enough to the singularity, but "close enough" here means roughly within a Planck length (or more appropriately a Planck time, since the singularity is really a moment of time)..

When claiming Planck length, Is that "size" up for further study?

Physicists are undecided whether the prediction of singularities means that they actually exist, or the current knowledge is insufficient to describe what happens at such extreme densities.

Sorry for the questions Peter I'm very curious here.

 

[PeterDonis]

Does that take into account the Final parsec problem?

What is the Final parsec problem?

When claiming Planck length, Is that "size" up for further study?

It's not experimentally verified, if that's what you mean. Since the smallest length and time scales we can probe experimentally are about 20 orders of magnitude larger than the Planck length/time, we have no prospect of testing at what specific length and time scale GR breaks down any time soon. The Planck length/time is just the most obvious quantity with length/time dimensions that you can make out of the relevant fundamental constants ($\hbar$, $G$, and $c$), so it's the obvious guess to make.

Physicists are undecided whether the prediction of singularities means that they actually exist, or the current knowledge is insufficient to describe what happens at such extreme densities.

Are you asking if this is true? I don't think it is; I think pretty much all physicists believe that singularities don't "actually exist"; they're signs that our existing theories break down in those regimes and we need to find new theories (i.e., that our current knowledge is insufficient for these regimes).

 

[Outhouse]

What is the Final parsec problem?

[as I understand] When two black are merging the problem is how they merge so quickly.

When two galaxies collide, the supermassive black holes at their centers do not hit head-on, but would shoot past each other if some mechanism did not bring them together. The most important mechanism is dynamical friction, which brings the black holes to within a few parsecs of each other. At this distance, they form a bound, binary system which must lose orbital energy somehow before the black holes can merge.[15]

Initially, the black holes transfer energy to the gas and stars between them, ejecting matter at high speed via a gravitational slingshot and thereby losing energy. However, the volume of space subject to this effect shrinks as the orbits do, and when the black holes reach a separation of about one parsec, there is so little matter left between them that it is not clear how they can continue to lose energy fast enough to merge within the age of the universe. Gravitational waves are not a significant contributor until the separation shrinks to a much smaller value, roughly 0.01–0.001 parsec.

 

[PeterDonis]

What you posted appears to be taken from here:

https://en.wikipedia.org/wiki/Binary_black_hole#Final_parsec_problem

(Note: if you're posting direct quotes from someplace, always give a link and always make it clear that it's a direct quote. I only found this page because one of the links in what you posted, the one to footnote 15 of the article, happened to give the article's URL.)

I see the issue being discussed, but it's not relevant to what I said about no material being lost when black holes merge. I was talking about the actual merger (since that's what was being discussed in the post I was responding to), not how the two holes get close enough to merge.

 

[Outhouse]

It's not experimentally verified, if that's what you mean.

What I mean is more in a question form of,,,, Do we really know that a singularity is a Planck sized pinpoint of infinite density inside the center of the event horizon of a black hole. Does a singularity actually exist in a black hole? Sorry to bother you with this, Ill try reading up on those who question it. Didn't mean to derail the thread.

 

[phinds]

What I mean is more in a question form of,,,, Do we really know that a singularity is a ...

"Singularity MEANS we don't know what is going on, so no.

 

[PeterDonis]

Do we really know that a singularity is a Planck sized pinpoint of infinite density inside the center of the event horizon of a black hole. Does a singularity actually exist in a black hole?

The answer to all of these is "we don't know". As I said, we can't even come close to probing this regime experimentally, so anything we can say about it is speculation at this point.

 

[timmdeeg]

The answer to all of these is "we don't know". As I said, we can't even come close to probing this regime experimentally, so anything we can say about it is speculation at this point.

Supposed once a theory of quantum gravity reconciles general relativity with quantum mechanics in a consistent mathematical way. Then I think the mathematical consistency would be a strong argument that this theory is correct, but nevertheless its theoretical predictions can't be confirmed experimentally.

How strong does the latter weaken the consistency argument and are there cases known in the past that a physical problem seemed to be solved from a mathematical point of view which however has turned out later to be wrong?

 

[Outhouse]

Singularity MEANS we don't know what is going on, so no.

I use that line all the time, but in this case, not sure why many/we even define a black hole as containing a singularity.

 

[Outhouse]

so anything we can say about it is speculation at this point.

This is exactly where the next advancement will be made, in our lifetime a working "hypothetical" TOE will come forward.

Can only hope partial test would be able to confirm enough to retain plausibility.

 

[Ibix]

I use that line all the time, but in this case, not sure why many/we even define a black hole as containing a singularity.

We don't, strictly speaking. We say that GR models a black hole as containing a singularity, but we have reason to believe that this means that GR goes wrong somewhere along the way.

 

[jbriggs444]

I use that line all the time, but in this case, not sure why many/we even define a black hole as containing a singularity.

Our mathematical description of a black hole has a feature which we term a "singularity". To say that this means that a black hole "contains" a singularity is, perhaps, an abuse of terminology, but it is a common abuse.

 

[PeterDonis]

How strong does the latter weaken the consistency argument

It is true that having a single self-consistent theory that accounts for all known experimental data carries weight; having one theory that has GR and our current quantum field theory as special cases--approximations valid under particular conditions--would be better, by some criteria, than just having the two separate theories, even if there were no experimental data that could not be accounted for by one of the two separate theories. But I don't know how you would quantify this.

are there cases known in the past that a physical problem seemed to be solved from a mathematical point of view which however has turned out later to be wrong?

Sure. Newtonian mechanics. It accounted for all the known experimental data when it was formulated, and for at least a century afterwards, and it unified at least two domains--falling bodies on Earth and motions of the Sun, planets, and Moon--that were previously covered by separate theories (roughly speaking, the mechanics implied by Galileo's experiments with inclined planes, and Kepler's model of the solar system), without any new experimental data that could not be accounted for by one of those two theories. But Newton's model was a clear unification of all that was known at that time about mechanics--yet, as we now know, it is not correct, it's just an approximation valid in a particular regime.

 

[timmdeeg]

It is true that having a single self-consistent theory that accounts for all known experimental data carries weight; having one theory that has GR and our current quantum field theory as special cases--approximations valid under particular conditions--would be better, by some criteria, than just having the two separate theories, even if there were no experimental data that could not be accounted for by one of the two separate theories. But I don't know how you would quantify this.

Perhaps it depends on how the singularity problem can be solved. Perhaps it might be even more convincing if it could be shown that gravity is an emergent phenomenon which reproduces General Relativity. Or do you think that it is quite compelling that QFT should be a special case?

Sure. Newtonian mechanics.

Ah yes. Whereby fortunately in this case the range of validity could investigated experimentally.

Thank you for your comments!

EDIT I'm realizing "perhaps" is just speculation, so please ignore it.

 

[Teslascience]

Where? Please give a reference.

Sorry, can't remember or find it again. It was years before.