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#1
12-03-2006, 06:03 AM
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Re: How do gravitons escape a black hole?
[ QUOTE ]
[ 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." 
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#2
12-03-2006, 06:30 AM
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Re: How do gravitons escape a black hole?
[ QUOTE ]
[ QUOTE ] [ 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 ] 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.
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#3
12-04-2006, 04:52 PM
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Re: How do gravitons escape a black hole?
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.
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#4
12-04-2006, 05:11 PM
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Re: How do gravitons escape a black hole?
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.
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#5
12-04-2006, 07:12 PM
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Re: How do gravitons escape a black hole?
[ 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?
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#6
12-04-2006, 05:15 PM
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Re: How do gravitons escape a black hole?
[ 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.
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#8
12-04-2006, 10:53 PM
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Re: How do gravitons escape a black hole?
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.
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#9
12-04-2006, 11:00 PM
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Re: How do gravitons escape a black hole?
[ 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.
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#10
12-07-2006, 10:38 AM
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Re: How do gravitons escape a black hole?
[ 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?
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