[math-fun] GR black hole collider ?
After looking at all the formulae re black holes, I have another question: If you could somehow accelerate 2 approximately equal black holes in a counter-rotating ring like CERN and have them smash into one another, what would happen? I'm talking about _pure_ GR here, so I'm not concerned about all of the cascade of random particles that you'd get just from a high energy collision, but I'm interested in what happens to the black holes themselves. I can think of 3 possibilities: 1. The black holes merge, producing one extremely fast rotating black hole. 2. The black holes miss one another, but scatter elastically, generating a significant gravitational wave. 3. The black holes rip one another "apart" (whatever that means), producing a shower of smaller black holes. I'm particularly interested if there are any solutions in GR of type 3.
On 10/21/2013 9:38 AM, Henry Baker wrote:
After looking at all the formulae re black holes, I have another question:
If you could somehow accelerate 2 approximately equal black holes in a counter-rotating ring like CERN and have them smash into one another, what would happen?
Interesting question. It could even be tried if we could make small, charged black holes.
I'm talking about _pure_ GR here, so I'm not concerned about all of the cascade of random particles that you'd get just from a high energy collision, but I'm interested in what happens to the black holes themselves.
I can think of 3 possibilities:
1. The black holes merge, producing one extremely fast rotating black hole.
Since the kinetic energy would go into the merged BH it would be a lot bigger than just the sum of the masses. There's a limit to how great the angular momentum can be so if the impact parameter was too great then you'd get something like 2 or 3, instead of a merged BH.
2. The black holes miss one another, but scatter elastically, generating a significant gravitational wave.
Of course the gravitational wave would carry away mass-energy, so the collision would not be elastic.
3. The black holes rip one another "apart" (whatever that means), producing a shower of smaller black holes.
I'm particularly interested if there are any solutions in GR of type 3.
I don't think so because that would imply a decrease in entropy. But that depends on the quasi-classical analysis of Beckenstein & Hawking, so it might well be wrong in the hoped for quantum theory of spacetime. Brent
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
----- No virus found in this message. Checked by AVG - www.avg.com Version: 2014.0.4158 / Virus Database: 3614/6765 - Release Date: 10/19/13
I think that such a collider would be far cheaper to build inside a supercomputer in the foreseeable future, so we wouldn't need to have charged black holes, or even counter-rotating rings. At 03:21 PM 10/21/2013, meekerdb wrote:
On 10/21/2013 9:38 AM, Henry Baker wrote:
After looking at all the formulae re black holes, I have another question:
If you could somehow accelerate 2 approximately equal black holes in a counter-rotating ring like CERN and have them smash into one another, what would happen?
Interesting question. It could even be tried if we could make small, charged black holes.
On 10/21/2013 4:25 PM, Henry Baker wrote:
I think that such a collider would be far cheaper to build inside a supercomputer in the foreseeable future, so we wouldn't need to have charged black holes, or even counter-rotating rings.
Except we don't know the equations of quantum gravity. So we could only simulate the GR collision, which for smaller BHs we're sure leaves out important stuff. The LIGO project has already done a lot of simulations of realistic mass BHs colliding - although I don't know that they've considered near light speed collisions. Brent
At 03:21 PM 10/21/2013, meekerdb wrote:
On 10/21/2013 9:38 AM, Henry Baker wrote:
After looking at all the formulae re black holes, I have another question:
If you could somehow accelerate 2 approximately equal black holes in a counter-rotating ring like CERN and have them smash into one another, what would happen? Interesting question. It could even be tried if we could make small, charged black holes.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
----- No virus found in this message. Checked by AVG - www.avg.com Version: 2014.0.4158 / Virus Database: 3614/6765 - Release Date: 10/19/13
And so, what happens? --Dan On 2013-10-21, at 5:57 PM, meekerdb wrote:
Except we don't know the equations of quantum gravity. So we could only simulate the GR collision, which for smaller BHs we're sure leaves out important stuff. The LIGO project has already done a lot of simulations of realistic mass BHs colliding - although I don't know that they've considered near light speed collisions.
It depends http://www.newscientist.com/article/dn9012-black-holes-collide-in-the-best-s... Brent On 10/21/2013 7:10 PM, Dan Asimov wrote:
And so, what happens?
--Dan
On 2013-10-21, at 5:57 PM, meekerdb wrote:
Except we don't know the equations of quantum gravity. So we could only simulate the GR collision, which for smaller BHs we're sure leaves out important stuff. The LIGO project has already done a lot of simulations of realistic mass BHs colliding - although I don't know that they've considered near light speed collisions.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
----- No virus found in this message. Checked by AVG - www.avg.com Version: 2014.0.4158 / Virus Database: 3614/6765 - Release Date: 10/19/13
While angular momentum is extremely important for simulation of 500,000-Sun BH's, I seriously doubt that quantum mechanics are either modelled or have any effect on BH's of this size. I understand why LIGO wants to do this: because they want to learn what to look for in gravitational waves so they can win a Nobel prize for "seeing" these gravitational waves. But my interest is completely different: I'm interested in learning about completely new solutions to the GR equations. There's a guy at Cambridge Univ. who's been doing some of the best N-body simulations; I'm going to try to ask him what the current state of play is. At 10:05 PM 10/21/2013, meekerdb wrote:
It depends
http://www.newscientist.com/article/dn9012-black-holes-collide-in-the-best-s...
Brent
On 10/21/2013 7:10 PM, Dan Asimov wrote:
And so, what happens?
--Dan
On 2013-10-21, at 5:57 PM, meekerdb wrote:
Except we don't know the equations of quantum gravity. So we could only simulate the GR collision, which for smaller BHs we're sure leaves out important stuff. The LIGO project has already done a lot of simulations of realistic mass BHs colliding - although I don't know that they've considered near light speed collisions.
On 10/22/2013 4:17 AM, Henry Baker wrote:
While angular momentum is extremely important for simulation of 500,000-Sun BH's, I seriously doubt that quantum mechanics are either modelled or have any effect on BH's of this size. I know it isn't modeled and I agree it wouldn't have any significant effect.
Brent
I understand why LIGO wants to do this: because they want to learn what to look for in gravitational waves so they can win a Nobel prize for "seeing" these gravitational waves.
But my interest is completely different: I'm interested in learning about completely new solutions to the GR equations.
There's a guy at Cambridge Univ. who's been doing some of the best N-body simulations; I'm going to try to ask him what the current state of play is.
At 10:05 PM 10/21/2013, meekerdb wrote:
It depends
http://www.newscientist.com/article/dn9012-black-holes-collide-in-the-best-s...
Brent
On 10/21/2013 7:10 PM, Dan Asimov wrote:
And so, what happens?
--Dan
On 2013-10-21, at 5:57 PM, meekerdb wrote:
Except we don't know the equations of quantum gravity. So we could only simulate the GR collision, which for smaller BHs we're sure leaves out important stuff. The LIGO project has already done a lot of simulations of realistic mass BHs colliding - although I don't know that they've considered near light speed collisions.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
----- No virus found in this message. Checked by AVG - www.avg.com Version: 2014.0.4158 / Virus Database: 3614/6765 - Release Date: 10/19/13
I did some more Googling & found that this is a subject of active research; i.e., no one knows what happens when a fast-spinning black hole acquires too much material. Specifically, a spinning black hole is known as a "Kerr black hole", and there is a "Kerr Limit" to how fast a Kerr black hole can spin. One of the problems of an "extreme" Kerr black hole (a Kerr black hole having maximum spin) is that the singularity -- which is a circular ring for a Kerr black hole -- approaches the event horizon from the inside and lies on the surface for an extreme Kerr black hole. But nature is apparently modest; "cosmic censorship" is invoked to hide all singularities behind event horizons. Cosmic censorship would imply that extreme Kerr black holes cannot exist. So what happens to a Kerr black hole that somehow gets too big? How does it disintegrate? No one knows. Apparently, a Kerr black hole cannot accumulate material incrementally; the physics seems to push particles away when the Kerr black hole approaches the Kerr limit. But no one knows if similar sized black holes can merge to form an extreme Kerr black hole. Kerr black holes carry up to 29% of their energy in their spin; ALL of this energy can be extracted (thereby producing a spinless black hole) using techniques such as a "Penrose process"; however, extracting all of this energy may take an infinite amount of time. Kerr black holes "frame drag" their surrounding space-time, so that it is impossible to remain stationary next to a Kerr black hole, no matter how much thrust your rocket has. Since all of the spin energy of a Kerr black hole can be extracted, this energy obviously lies OUTSIDE the event horizon within the "dragged frame". Ditto for the angular momentum ?? Because the singularity of a Kerr black hole is a circular ring, it should be possible to go through it. Unfortunately, all of this happens inside the event horizon so you wouldn't be able to communicate any results to anyone outside. There are apparently "closed timelike curves" (CTC's) associated with Kerr black holes, which might conceivably be connected with "time travel". http://en.wikipedia.org/wiki/Closed_timelike_curve There's even a really cool, but really far-out proposal called "A symmetric matter-antimatter Milne Universe", in which particles like electrons are little Kerr black holes (with charge, obviously): From: http://www.icranet.org/talks/WeeklySeminars/2008/March/Chardin.pdf To: D:\Downloads\Chardin.pdf Size: 11.2 MB (11,731,792 bytes) From: http://moriond.in2p3.fr/J08/trans/sunday/benoit-levy.pdf To: D:\Downloads\benoit-levy.pdf Size: 2.1 MB (2,116,521 bytes) From: http://indico.lal.in2p3.fr/getFile.py/access?resId=2&materialId=slides&confI... To: D:\Downloads\Milne_Chardin_LAL.pdf Size: 1.4 MB (1,451,264 bytes)
Wouldn't an electron-black hole evaporate (essentially) instantly through Hawking radiation? The Schwarzschild evaporation time would be https://www.google.com/search?q=mass+of+an+electron ^3+*+5120*2*pi^2*G^2%2F%28Planck%27s+constant*c^4%29 I don't know the equivalent Kerr-Newman equation (maybe someone can help me out here?) but I wouldn't expect it to be much longer. Surely there is an answer, else this solution would not have been proposed. Charles Greathouse Analyst/Programmer Case Western Reserve University On Tue, Oct 22, 2013 at 4:05 PM, Henry Baker <hbaker1@pipeline.com> wrote:
I did some more Googling & found that this is a subject of active research; i.e., no one knows what happens when a fast-spinning black hole acquires too much material.
Specifically, a spinning black hole is known as a "Kerr black hole", and there is a "Kerr Limit" to how fast a Kerr black hole can spin. One of the problems of an "extreme" Kerr black hole (a Kerr black hole having maximum spin) is that the singularity -- which is a circular ring for a Kerr black hole -- approaches the event horizon from the inside and lies on the surface for an extreme Kerr black hole.
But nature is apparently modest; "cosmic censorship" is invoked to hide all singularities behind event horizons. Cosmic censorship would imply that extreme Kerr black holes cannot exist.
So what happens to a Kerr black hole that somehow gets too big? How does it disintegrate? No one knows.
Apparently, a Kerr black hole cannot accumulate material incrementally; the physics seems to push particles away when the Kerr black hole approaches the Kerr limit. But no one knows if similar sized black holes can merge to form an extreme Kerr black hole.
Kerr black holes carry up to 29% of their energy in their spin; ALL of this energy can be extracted (thereby producing a spinless black hole) using techniques such as a "Penrose process"; however, extracting all of this energy may take an infinite amount of time.
Kerr black holes "frame drag" their surrounding space-time, so that it is impossible to remain stationary next to a Kerr black hole, no matter how much thrust your rocket has. Since all of the spin energy of a Kerr black hole can be extracted, this energy obviously lies OUTSIDE the event horizon within the "dragged frame". Ditto for the angular momentum ??
Because the singularity of a Kerr black hole is a circular ring, it should be possible to go through it. Unfortunately, all of this happens inside the event horizon so you wouldn't be able to communicate any results to anyone outside.
There are apparently "closed timelike curves" (CTC's) associated with Kerr black holes, which might conceivably be connected with "time travel".
http://en.wikipedia.org/wiki/Closed_timelike_curve
There's even a really cool, but really far-out proposal called "A symmetric matter-antimatter Milne Universe", in which particles like electrons are little Kerr black holes (with charge, obviously):
From: http://www.icranet.org/talks/WeeklySeminars/2008/March/Chardin.pdf To: D:\Downloads\Chardin.pdf Size: 11.2 MB (11,731,792 bytes)
From: http://moriond.in2p3.fr/J08/trans/sunday/benoit-levy.pdf To: D:\Downloads\benoit-levy.pdf Size: 2.1 MB (2,116,521 bytes)
From: http://indico.lal.in2p3.fr/getFile.py/access?resId=2&materialId=slides&confI... To: D:\Downloads\Milne_Chardin_LAL.pdf Size: 1.4 MB (1,451,264 bytes)
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (4)
-
Charles Greathouse -
Dan Asimov -
Henry Baker -
meekerdb