How do gravitons escape a black hole?

[Metric]

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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.

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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)

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And has a "graviton producing machine" any meaning?

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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).

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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.

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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!

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

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Right.

[Charon]

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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).


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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?

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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!


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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]

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

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

[Skidoo]

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

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

[Metric]

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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?

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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.

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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!

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

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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]

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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.

[Charon]

See my reply to Skidoo.

[Skidoo]

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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/sh...2586&page=