How do gravitons escape a black hole?

[thylacine]

How do gravitons escape a black hole?

How does gravity escape a black hole?

[Skidoo]

How does any interaction cross the event horizon?

[AWoodside]

This is a really good question and I'll tell you what I think about it. I'm not 100% confident of my understanding on the matter and would welcome any corrections or criticisms.

Unfortunately, the answer may boil down to the fact that we just don't have a good quantum gravity theory yet so we aren't yet equipped theoretically to answer this question.

One way to look at it is from a general relativity perspective. In GR, "gravity" is just the result of the curvature of space-time. There are no gravitons that need to escape and black holes are just an extremely curvy bit of space-time. Gravity in GR isn't something that travels like photons, it is a property of space itself.

For a theory of gravitons it is trickier. I would attribute it to quantum tunneling. Quantum mechanical particles can overcome potential barriers that classical particles can not, due to the uncertainty principle. This property, often called tunneling, is responsible for a phenomenon known as Hawking radiation, which is basically a radiation of photons every black hole gives off. I'd imagine a similar thing could happen for gravitons.

[GMontag]

Virtual particles aren't limited to the speed of light. In the same way that virtual photons can escape a charged black hole to mediate the electromagnetic field, virtual gravitons can escape to mediate the gravitational field.

We don't actually have a full theory of gravitons, so we don't really know if actual gravitons (i.e. gravitational waves) travel at the speed of light, or are even affected by gravity, but both are common assumptions. Anyway, actual gravitons would only be produced *outside* the event horizon, (e.g. by two black holes circling each other before collision) and so would still be able to escape.

[Jcrew]

Gravitons are predicted by quantum theory and black holes by GR. Since QT and GR aren't compatible not sure if you can take one object from one framework and put it in another.

[whatnow1080]

[ QUOTE ]
How does any interaction cross the event horizon?

[/ QUOTE ]
I'm not sure if anything can actually cross the event horizon. I haven't read up on physics lately, but from what I remember the curvature of space becomes infinite at the event horizon and time stops, so I would think that things just get stuck at the event horizon. Any experts please feel free to correct me on this.

[thylacine]

A couple of good responses so far. Let's expand the list of questions.

1. How do gravitons escape a black hole?

2. How does gravity escape a black hole?

3. Is there anything special about the event horizon?

4. If there is a graviton version of Hawking radiation, call it graviton-Hawking-radiation, then what is its strength?

5. Is the strength of the graviton-Hawking-radiation basically the same strength as the gravity (gravitational acceleration) itself? (Set hbar, c, G to 1.)

6. If so, or if not, what role does graviton-Hawking-radiation play in gravity?

7. Since Hawking radiation comes from gravitional acceleration, does it not occur also inside the event horizon all the way down to the `singularity'?

Here `singularity' means whatever there is in quantum gravity in place of the classical singularity of GR (general relativity).

8. If not, then how does all the mass get from the `singularity' to the outside during the complete Hawking evaporation of a black hole via Hawking radiation?

9. If so, how much of the mass of the black hole consists of Hawking radiation between the `singularity' and the event horizon?

10. If you are accelerating `forwards' in space, does the Unruh radiation (similar concept to Hawking radiation, relating gravity to acceleration) hit you from the front or the back, or from all around, or what?

11. What are all the similarities, and differences, between gravitons and photons?

12. (For genuine experts only) how much of the above is nonsense based on ignorance?

[Metric]

[ QUOTE ]
A couple of good responses so far. Let's expand the list of questions.

1. How do gravitons escape a black hole?

[/ QUOTE ]
A "graviton producing machine" inside the BH will not be able to send real gravitons out past the event horizon. (provided we remain in the limit where the BH solution can be thought of as a reasonable background)

[ QUOTE ]
2. How does gravity escape a black hole?

[/ QUOTE ]
Gravity doesn't "escape" a black hole -- a black hole *is* a solution to the gravitational field equations.

[ QUOTE ]
3. Is there anything special about the event horizon?

[/ QUOTE ]
Not locally -- you wouldn't notice anything special if you were in a box falling across the horizon. Outside the BH, though, it does have significance -- you'll never hear again from anything that crosses the horizon.

[ QUOTE ]
4. If there is a graviton version of Hawking radiation, call it graviton-Hawking-radiation, then what is its strength?

[/ QUOTE ]
It should exist, and it should have a thermal spectrum just like any other field (provided again that the BH solution can be thought of as a good background -- i.e. the perturbative regime -- this should be an extremely good approximation for any reasonable BH, though).

[ QUOTE ]
5. Is the strength of the graviton-Hawking-radiation basically the same strength as the gravity (gravitational acceleration) itself? (Set hbar, c, G to 1.)

[/ QUOTE ]
The temperature defining the thermal spectrum of gravitons should be proportional to the surface gravity of the BH (which will be inversely proportional to the mass of the BH).

[ QUOTE ]
6. If so, or if not, what role does graviton-Hawking-radiation play in gravity?

[/ QUOTE ]
Due to the weakness of Hawking radiation, the gravitons can be thought of as tiny perturbations to the BH solution -- they shouldn't be significant in changing the causal structure of the BH solution.

[ QUOTE ]
7. Since Hawking radiation comes from gravitional acceleration, does it not occur also inside the event horizon all the way down to the `singularity'?

[/ QUOTE ]
I seem to recall that a freely falling detector dropped into a BH isn't excited by Hawking radiation, but I could be mistaken.

[ QUOTE ]
8. If not, then how does all the mass get from the `singularity' to the outside during the complete Hawking evaporation of a black hole via Hawking radiation?

[/ QUOTE ]
Hawking radiation is a property of the vacuum outside the BH -- there are some problems with thinking of Hawking radiation as something "escaping" from the BH. That said, there are some very big problems associated with "complete evaporation" of a BH that aren't properly understood by anyone.

[ QUOTE ]
9. If so, how much of the mass of the black hole consists of Hawking radiation between the `singularity' and the event horizon?

[/ QUOTE ]
This is a sort of ill-defined question. The BH's mass is defined with respect to a "timelike Killing vector" that doesn't exist inside the BH. Energy and momentum inside the BH are only locally defined concepts.

[ QUOTE ]
10. If you are accelerating `forwards' in space, does the Unruh radiation (similar concept to Hawking radiation, relating gravity to acceleration) hit you from the front or the back, or from all around, or what?

[/ QUOTE ]
It's isotropic.

[ QUOTE ]
11. What are all the similarities, and differences, between gravitons and photons?

[/ QUOTE ]
This could lead to a huge, detailed discussion in and of itself. If you want to discuss it more, I wouldn't mind doing so, but I'll sidestep it for this particular post.

[ QUOTE ]
12. (For genuine experts only) how much of the above is nonsense based on ignorance?

[/ QUOTE ]
They seem like reasonable questions, but as always a more detailed understanding reveals some "problems" to not be problems at all, and some questions not to be defined in the original sense that you imagined.

[theblackkeys]

Gravitons exist?

[John21]

[ QUOTE ]
Gravitons exist?

[/ QUOTE ]

Only inside fuzzballs (http://www.sciencedaily.com/releases/2004/03/040304073931.htm)

[Metric]

[ QUOTE ]
Gravitons exist?

[/ QUOTE ]
They haven't been directly detected yet (due to limitations on experimental technology), but if they don't exist something is seriously wrong with our understanding of physics.

[Skidoo]

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3. Is there anything special about the event horizon?

[/ QUOTE ]Not locally -- you wouldn't notice anything special if you were in a box falling across the horizon.

[/ QUOTE ]

Perhaps in the ideal case, but there would be a gigantic tidal force due to the gravitational gradients in a box with a non-negligible height. Also, at some point in such a compartment, the event horizon would be between the floor and ceiling, which could produce some interesting effects.

[Magic_Man]

[ QUOTE ]
This property, often called tunneling, is responsible for a phenomenon known as Hawking radiation, which is basically a radiation of photons every black hole gives off. I'd imagine a similar thing could happen for gravitons.

[/ QUOTE ]

I could be wrong about this, but I thought Hawking radiation occurred as follows (please forgive my simplification; I understand this stuff mostly from books like "A Brief History of Time" and not from real astrophysics studies):

It is known that at the smallest space and time scales, matter-antimatter pairs can pop into existence and immediately annihilate afterwards. Hawking radiation occurs when this interaction happens at the event horizon. A pair pops into existence, and one of the pair is sucked into the black hole. The other one is given a boost of energy that is enough to kick it away from the black hole, and voila, you get Hawking radiation.

Is it possible that this same thing is occurring with gravitons?

~MagicMan

[Metric]

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[ QUOTE ]
[ QUOTE ]
3. Is there anything special about the event horizon?

[/ QUOTE ]Not locally -- you wouldn't notice anything special if you were in a box falling across the horizon.

[/ QUOTE ]

Perhaps in the ideal case, but there would be a gigantic tidal force due to the gravitational gradients in a box with a non-negligible height.

[/ QUOTE ]
The tidal forces are there regardless of the horizon (both inside and outside the horizon of a BH, and they are there even if the gravitating object isn't a BH), and with a large enough BH you wouldn't even notice them at the horizon.

[ QUOTE ]
Also, at some point in such a compartment, the event horizon would be between the floor and ceiling, which could produce some interesting effects.

[/ QUOTE ]
No, not to a freely falling observer. If, however, you activated "sooper dooper rockets" located on the top and bottom of your box precisely at this moment, the top could in principle escape to infinity while the bottom could never break free. The horizon is not defined via local effects -- it is defined via the global properties of a spacetime as "the boundary of the past of future null infinity."

[Skidoo]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
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3. Is there anything special about the event horizon?

[/ QUOTE ]Not locally -- you wouldn't notice anything special if you were in a box falling across the horizon.

[/ QUOTE ]

Perhaps in the ideal case, but there would be a gigantic tidal force due to the gravitational gradients in a box with a non-negligible height.

[/ QUOTE ]
The tidal forces are there regardless of the horizon (both inside and outside the horizon of a BH, and they are there even if the gravitating object isn't a BH), and with a large enough BH you wouldn't even notice them at the horizon.

[/ QUOTE ]

Okay. The tidal forces at a given distance can be reduced by increasing the radius of the BH or whatever.

[ QUOTE ]
[ QUOTE ]
Also, at some point in such a compartment, the event horizon would be between the floor and ceiling, which could produce some interesting effects.

[/ QUOTE ]
No, not to a freely falling observer. If, however, you activated "sooper dooper rockets" located on the top and bottom of your box precisely at this moment, the top could in principle escape to infinity while the bottom could never break free. The horizon is not defined via local effects -- it is defined via the global properties of a spacetime as "the boundary of the past of future null infinity."

[/ QUOTE ]

I see where you're coming from that in principle a falling observer can't notice anything different in his frame of reference, but I think this is an ideal situation that wouldn't exist in reality. As any compartment with a finite height crosses the event horizon, a light beam directed laterally near the floor would take a closed path while a similar beam near the ceiling could still escape to an indefinite distance.

[Skidoo]

[ QUOTE ]
Okay. The tidal forces at a given distance can be reduced by increasing the radius of the BH or whatever.

[/ QUOTE ]

Wrong.

[theblackkeys]

[ QUOTE ]
[ QUOTE ]
Gravitons exist?

[/ QUOTE ]

Only inside fuzzballs (http://www.sciencedaily.com/releases/2004/03/040304073931.htm)

[/ QUOTE ]
I'm so glad I don't sttudy physics.

[thylacine]

Thanks, Metric for detailed responses. Thanks to others too.

I have tons of questions but let me focus on one key question.

Let's assume the mass (and maybe charge and angular momentum) of a black hole is concentrated at the `singularity'?

Again, here `singularity' means whatever there is in quantum gravity in place of the classical singularity of GR.

Suppose it is a big black hole, so the event horizon is a long way from the `singularity'.

Then in the Hawking evaporation of the black hole (assume nothing is falling in, and don't worry about final stages for now) it seems to me that the mass (and maybe charge and angular momentum) must come not just from around the event horizon, but instead must makes its way out all the way from the `singularity', meaning that there is a flow of mass (and maybe charge and angular momentum) from the `singularity' all the way out to the event horizon and beyond.

QUESTION: Is something like this what is actually happening?

Moreover the strength of this flow should be calculable from standard formulas relating strength of Hawking/Unruh radiation to acceleration (gravitational or otherwise).
So the Hawking/Unruh radiation is stronger nearer the `singularity'. And it has mass. Maybe all of the mass is in this form leaving no singularity!

By the way, I assume that the principle of equivalence (relating acceleration and gravitational acceleration) means that Hawking and Unruh radiation are basically the same thing, and that freely falling bodies (anywhere, not just in a black hole) don't see it. But I don't think the observations of a freefaller in a black hole rule out what I said above.

[Upstairs]

One way to think of the way gravity curves spacetime is to picture a bedsheet on your bed with different sized ball bearings on it representing stars. Now put a bowling ball representing a massive black hole in the middle. Well... the smaller bearings are going to roll towards it.

You see, there is no comminication between the bowling ball and the ball bearings at all, but they *are* affected by each other. The key concept here is that *gravity warps spacetime* just like that bowling ball warps your bedsheet.

[Upstairs]

[ QUOTE ]
Then in the Hawking evaporation of the black hole (assume nothing is falling in, and don't worry about final stages for now) it seems to me that the mass (and maybe charge and angular momentum) must come not just from around the event horizon, but instead must makes its way out all the way from the `singularity', meaning that there is a flow of mass (and maybe charge and angular momentum) from the `singularity' all the way out to the event horizon and beyond.

QUESTION: Is something like this what is actually happening?

[/ QUOTE ]

The event horizon *is* the singularity / where the singularity occurs.

[BigBuffet]

[ QUOTE ]
One way to think of the way gravity curves spacetime is to picture a bedsheet on your bed with different sized ball bearings on it representing stars. Now put a bowling ball representing a massive black hole in the middle. Well... the smaller bearings are going to roll towards it.

You see, there is no comminication between the bowling ball and the ball bearings at all, but they *are* affected by each other. The key concept here is that *gravity warps spacetime* just like that bowling ball warps your bedsheet.

[/ QUOTE ]

Wouldn't the bigger ball bearings roll toward and then hit the bowling ball first thus causing the smaller ball bearings to ricochet off them back in the direction they came from?

[Metric]

[ QUOTE ]
The event horizon *is* the singularity / where the singularity occurs.

[/ QUOTE ]
No, it's not.

[Skidoo]

Space aside, the question remains as to just how there could be a causal relationship of any sort between something, even a quantity of mass per se, within the critical radius and the outside world.

[Metric]

[ QUOTE ]
Let's assume the mass (and maybe charge and angular momentum) of a black hole is concentrated at the `singularity'?

Suppose it is a big black hole, so the event horizon is a long way from the `singularity'.

Then in the Hawking evaporation of the black hole (assume nothing is falling in, and don't worry about final stages for now) it seems to me that the mass (and maybe charge and angular momentum) must come not just from around the event horizon, but instead must makes its way out all the way from the `singularity', meaning that there is a flow of mass (and maybe charge and angular momentum) from the `singularity' all the way out to the event horizon and beyond.

QUESTION: Is something like this what is actually happening?

[/ QUOTE ]
The standard understanding of the Hawking effect relies only on the properties of fields to the exterior of the BH. It doesn't depend on a flux of particles moving from the singularity to the horizon. In fact, if you try to make the "flux of particles" idea concrete, you quickly run into problems.

[ QUOTE ]
Moreover the strength of this flow should be calculable from standard formulas relating strength of Hawking/Unruh radiation to acceleration (gravitational or otherwise).
So the Hawking/Unruh radiation is stronger nearer the `singularity'. And it has mass. Maybe all of the mass is in this form leaving no singularity!

[/ QUOTE ]
Mass with respect to what? Outside the BH, "mass" makes sense with respect to a timelike Killing vector that defines symmetry with respect to time translations. Inside the BH, there is no such symmetry with which to define "mass" unambiguously.

[Upstairs]

[ QUOTE ]
[ QUOTE ]
The event horizon *is* the singularity / where the singularity occurs.

[/ QUOTE ]
No, it's not.

[/ QUOTE ]

I stand corrected.

[thylacine]

[ QUOTE ]
[ QUOTE ]
Let's assume the mass (and maybe charge and angular momentum) of a black hole is concentrated at the `singularity'?

Suppose it is a big black hole, so the event horizon is a long way from the `singularity'.

Then in the Hawking evaporation of the black hole (assume nothing is falling in, and don't worry about final stages for now) it seems to me that the mass (and maybe charge and angular momentum) must come not just from around the event horizon, but instead must makes its way out all the way from the `singularity', meaning that there is a flow of mass (and maybe charge and angular momentum) from the `singularity' all the way out to the event horizon and beyond.

QUESTION: Is something like this what is actually happening?

[/ QUOTE ]
The standard understanding of the Hawking effect relies only on the properties of fields to the exterior of the BH. It doesn't depend on a flux of particles moving from the singularity to the horizon. In fact, if you try to make the "flux of particles" idea concrete, you quickly run into problems.

[ QUOTE ]
Moreover the strength of this flow should be calculable from standard formulas relating strength of Hawking/Unruh radiation to acceleration (gravitational or otherwise).
So the Hawking/Unruh radiation is stronger nearer the `singularity'. And it has mass. Maybe all of the mass is in this form leaving no singularity!

[/ QUOTE ]
Mass with respect to what? Outside the BH, "mass" makes sense with respect to a timelike Killing vector that defines symmetry with respect to time translations. Inside the BH, there is no such symmetry with which to define "mass" unambiguously.

[/ QUOTE ]

Is this question `how does the mass get from the "singularity" to the outside?' something that, at least if formulated correctly (which could be the main difficulty) would be a serious and interesting physics question? Certainly there are many questions associated with the overall process.

Or is it as fundamentally wrongheaded as asking, say, `which slit did the photon go through?' (in the double-slit experiment)?

Or somewhere in between?

[Metric]

I would say that your question lies somewhere between "already answered" (energy leaves the BH because "negative energy" modes are falling in) and "not too well defined" (if you're wanting to do something like calculating how much of the BH mass lies in a particular extended region of the BH).

But you could probably morph your question into something very interesting indeed with a bit of work -- as you said, there are lots of puzzles here.

[thylacine]

[ QUOTE ]
I would say that your question lies somewhere between "already answered" (energy leaves the BH because "negative energy" modes are falling in) and "not too well defined" (if you're wanting to do something like calculating how much of the BH mass lies in a particular extended region of the BH).

But you could probably morph your question into something very interesting indeed with a bit of work -- as you said, there are lots of puzzles here.

[/ QUOTE ]

I tried reading something on QFT in curved spacetime once (and I don't really understand QFT to start with) and I vaguely remember there was some issue with defining "negative energy" modes to start with, whereas it is not a problem to canonically make a choice in standard QFT. Is this issue related to making what you said above work.

I vaguely see what the problems are with defining mass, (something along the lines of: Newton would integrate mass density over a 3D region, or do an equivalent surface integral, but there are some problems doing this in GR even though its worth a try) but I'll have to do some reading. My attempt to understand GR comes from reading "Spacetime and geometry : an introduction to general relativity" by Sean Carroll, which I found very good. I did not know what a differentiable manifold was before reading it.

Can you recommend a QFT book for a mathematician?

As for `"negative energy" modes are falling in' (? to the singularity) that's probably good enough for me in place of energy flowing out. I would just expect some kind of causal connectivity, which would be `local' in some sense. That's really what would prompt me to wonder how to bridge what I might perceive to be a (causal) gap between the singularity and the event-horizon.

[Metric]

[ QUOTE ]
tried reading something on QFT in curved spacetime once (and I don't really understand QFT to start with) and I vaguely remember there was some issue with defining "negative energy" modes to start with, whereas it is not a problem to canonically make a choice in standard QFT. Is this issue related to making what you said above work.

[/ QUOTE ]
This is related to that whole Killing vector issue I mentioned before. In flat spacetime, there's a canonical choice of positive energy modes (particles) due to the existence of a timelike Killing vector. This nice property goes away in general spacetimes. Or you may have a timelike Killing vector in one region of spacetime (outside the BH) and not in another (inside the BH).

[ QUOTE ]
I vaguely see what the problems are with defining mass, (something along the lines of: Newton would integrate mass density over a 3D region, or do an equivalent surface integral, but there are some problems doing this in GR even though its worth a try) but I'll have to do some reading. My attempt to understand GR comes from reading "Spacetime and geometry : an introduction to general relativity" by Sean Carroll, which I found very good. I did not know what a differentiable manifold was before reading it.

[/ QUOTE ]

If that's the relatively new book by Carroll based on his online GR notes, I agree that it's excellent. I would also recommend "A relativist's toolkit: the mathematics of black hole mechanics" by Eric Poisson if you want a great book to reference.

[ QUOTE ]
Can you recommend a QFT book for a mathematician?

[/ QUOTE ]

For what we're talking about here, "Quantum fields in curved space" by Birrell and Davies is the right place to go. You get the field theory without all the heavy formalism developed to do big calculations with the standard model, etc. (but on the other hand it's much heavier in the GR department of course) A great deal of the stuff (including Hawking's work) people have studied in the curved spacetime setting has just been done with super-simple, non-interacting scalar fields -- you don't need QCD to get at the general principles of what is going on.

For a more standard treatment of QFT, but with some good tidbits thrown in (like slick, three line derivations of the Hawking effect, etc.) get "Quantum Field Theory in a Nutshell" by Zee.

[Charon]

[ QUOTE ]
Quote:
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A couple of good responses so far. Let's expand the list of questions.

1. How do gravitons escape a black hole?


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A "graviton producing machine" inside the BH will not be able to send real gravitons out past the event horizon. (provided we remain in the limit where the BH solution can be thought of as a reasonable background)


[/ QUOTE ]

Isn't it true that virtual particles can travel faster than light as long as they don't violate the uncertainty principle? So if that is true, then gravitons can escape the event horizon as long as their velocity is high enough.

And has a "graviton producing machine" any meaning?
From my knowledge, virtal particles (like photon, Z-boson, W-boson) are obtained by quantizing the appropriate field, where every gauge transformation of the field corresponds to a different type of particle. The excitations of the gauge fields represent particles. So the field (in this case the gravitational field) can be described in terms of excitations (particles) which can be created and annihilated. It's not like the mass in the BH is constantly sending out gravitons. Am I correct?

Thanks.

[Metric]

[ QUOTE ]
Isn't it true that virtual particles can travel faster than light as long as they don't violate the uncertainty principle? So if that is true, then gravitons can escape the event horizon as long as their velocity is high enough.

[/ QUOTE ]

It is true that charge within a BH produces a field outside the BH. ("virtual particles" are basically just perturbative way of thinking about charges interacting)

[ QUOTE ]
And has a "graviton producing machine" any meaning?

[/ QUOTE ]
Sure -- in much the same way that a lightbulb is a photon producing machine. Oscillating charges make photons -- oscillating masses make gravitons (though it would be technologically much more difficult of course, and hasn't been done to date).

[ QUOTE ]
From my knowledge, virtal particles (like photon, Z-boson, W-boson) are obtained by quantizing the appropriate field, where every gauge transformation of the field corresponds to a different type of particle. The excitations of the gauge fields represent particles. So the field (in this case the gravitational field) can be described in terms of excitations (particles) which can be created and annihilated.

[/ QUOTE ]
It seems you have a good idea of what's going on -- the complication in this case is that in curved spacetime the concept of "particle" becomes less useful and sometimes isn't well defined. The field picture is still good, but the way you express excitations in the field can become arbitrary. So basically the "graviton picture" represents small quanta of purturbations to a fixed background spacetime with certain symmetries. Too many gravitons, though, and it may be that the fixed background isn't good anymore!

[ QUOTE ]
It's not like the mass in the BH is constantly sending out gravitons. Am I correct?

[/ QUOTE ]

Right.

[Charon]

[ QUOTE ]
Sure -- in much the same way that a lightbulb is a photon producing machine. Oscillating charges make photons -- oscillating masses make gravitons (though it would be technologically much more difficult of course, and hasn't been done to date).


[/ QUOTE ]

I was referring to a static BH. But even an oscillating BH wouldn't produce gravitons, since you need a quadrupole moment instead of a dipole moment. My guess is that a BH is spherically symmetric, so in that case even if it was oscillating it wouldn't produce a quadrupole moment. So you would need for instance another mass to create a quadrupole moment (and gravitons). Is this correct or am I missing something?

[ QUOTE ]
So basically the "graviton picture" represents small quanta of purturbations to a fixed background spacetime with certain symmetries. Too many gravitons, though, and it may be that the fixed background isn't good anymore!


[/ QUOTE ]

Does this refer to the inconsistency between quantum field theory, which is background dependent, and general relativity, which is background independent?

Thank you for your answer.

[thylacine]

[ QUOTE ]

Does this refer to the inconsistency between quantum field theory, which is background dependent, and general relativity, which is background independent?

[/ QUOTE ]

What exactly do the phrases "background dependent" and "background independent" refer to?

[Skidoo]

[ QUOTE ]
Does this refer to the inconsistency between quantum field theory, which is background dependent, and general relativity, which is background independent?

[/ QUOTE ]

If you're referring to the controversy over covariance, that's an interesting topic in itself.

[Metric]

[ QUOTE ]
I was referring to a static BH. But even an oscillating BH wouldn't produce gravitons, since you need a quadrupole moment instead of a dipole moment. My guess is that a BH is spherically symmetric, so in that case even if it was oscillating it wouldn't produce a quadrupole moment. So you would need for instance another mass to create a quadrupole moment (and gravitons). Is this correct or am I missing something?

[/ QUOTE ]
Let's go back to my original statement. "A 'graviton producing machine' inside the BH will not be able to send real gravitons out past the event horizon." I.E. if you fall inside the horizon and then turn on your graviton flashlight, none of those gravitons will escape the horizon. Your other comments are a different subject, but suffice it to say that black holes undergoing quasinormal oscillations can indeed generate gravitational waves, which if quantized should correspond to gravitons.

[ QUOTE ]
[ QUOTE ]
So basically the "graviton picture" represents small quanta of purturbations to a fixed background spacetime with certain symmetries. Too many gravitons, though, and it may be that the fixed background isn't good anymore!

[/ QUOTE ]
Does this refer to the inconsistency between quantum field theory, which is background dependent, and general relativity, which is background independent?

[/ QUOTE ]
Yes, I'd say it's probably the tip of that particular iceberg.

[Charon]

Thank you for your responses. I know I was touching a different subject, but I find this field of physics very interesting, so I couldn't resist ;-)

Regards

[Charon]

[ QUOTE ]
If you're referring to the controversy over covariance, that's an interesting topic in itself.

[/ QUOTE ]

No, I'm not referring to covariance. Quantum Mechanics can already be formulated in a covariant way, see for instance the Klein-Gordon and Dirac equations.

A big problem in constructing quantum field theories is the fact that the field operator does not make mathematical sense as an operator defined at each spacetime point, but must be interpreted as a distribution in spacetime. This corresponds to the physical fact that the field can not be measured at a single point; only averages of the field over spacetime regions are physically well-defined (see Wald, General Relativity). Now, if one considers interactions, this unavoidably leads to considering the products of field operators at the same spacetime point. Such quantities have no natural mathematical meaning.

To avoid this, you can treat interactions as pertubations of a well defined free field theory. But this requires the theory to be renormalizable, and thusfar all succesful quantum field theories are renormalizable.

General Relativity is different however. The essential difference between general relativity and other classical theories is the dual role played by the metric tensor as both the quantity that describes the dynamical aspects of gravity, but it also describes the background spacetime structure. Thus, in order to quantize the dynamical degrees of freedom of the gravitational field, one must also give a quantum mechanical description for the spacetime structure. Other QFTs don't have this problem, since they are formulated on a fixed background spacetime, which is treated classically.

I think what Metric meant was that as long as the gravitons respresent only small pertubations, one can ignore back-interaction and you can treat the QFT of gravity as a linear quantum matter field propagating in a fixed background curved spacetime. But too many gravitons, and this theory is no longer valid and you need a full quantum theory of gravity, with the problems described above.

[Charon]

See my reply to Skidoo.

[Skidoo]

[ QUOTE ]
[ QUOTE ]
If you're referring to the controversy over covariance, that's an interesting topic in itself.

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No, I'm not referring to covariance. Quantum Mechanics can already be formulated in a covariant way, see for instance the Klein-Gordon and Dirac equations.

A big problem in constructing quantum field theories is the fact that the field operator does not make mathematical sense as an operator defined at each spacetime point, but must be interpreted as a distribution in spacetime. This corresponds to the physical fact that the field can not be measured at a single point; only averages of the field over spacetime regions are physically well-defined (see Wald, General Relativity). Now, if one considers interactions, this unavoidably leads to considering the products of field operators at the same spacetime point. Such quantities have no natural mathematical meaning.

To avoid this, you can treat interactions as pertubations of a well defined free field theory. But this requires the theory to be renormalizable, and thusfar all succesful quantum field theories are renormalizable.

General Relativity is different however. The essential difference between general relativity and other classical theories is the dual role played by the metric tensor as both the quantity that describes the dynamical aspects of gravity, but it also describes the background spacetime structure. Thus, in order to quantize the dynamical degrees of freedom of the gravitational field, one must also give a quantum mechanical description for the spacetime structure. Other QFTs don't have this problem, since they are formulated on a fixed background spacetime, which is treated classically.

I think what Metric meant was that as long as the gravitons respresent only small pertubations, one can ignore back-interaction and you can treat the QFT of gravity as a linear quantum matter field propagating in a fixed background curved spacetime. But too many gravitons, and this theory is no longer valid and you need a full quantum theory of gravity, with the problems described above.

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Indeed (except for the last part about gravitons, which I'll go with as read).

The point of my comment was to prompt a post or two on concepts of space and how the absolute space of early days has developed at last into a spacetime in which coordinates are solved away and have no primitive identity.

The rise-and-fall of a reification always makes for an interesting read.

[Metric]

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The point of my comment was to prompt a post or two on concepts of space and how the absolute space of early days has developed at last into a spacetime in which coordinates are solved away and have no primitive identity.

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I posted an intro to general covariance a while back, which you may or may not have already seen...

http://forumserver.twoplustwo.com/showthreaded.php?Cat=0&Number=5812586&page=