In fact, spacetime behaves very well at singularities, in the old framework of General Relativity. Singularities occur, indeed, as Penrose and Hawking proved long time ago. But physics and differential geometry can be done there. Equivalent versions of Einstein's equation can be written. They give the same result as the standard Einstein equation where there are not singularities, but apply also where there are singularities. The singularities don't destroy information.
The stationary black holes admit coordinate systems which makes the singularity of the metric to be "benign", i.e. smooth and without infinities:
The singularities are compatible with global hyperbolicity and don't destroy information, if we know how to continue the equations beyond the singularities:
Hi Steve,
It was believed that nothing can escape the black holes, and then in 1974 Hawking realized that they can emit particles. The particles are not emitted from inside the black hole's event horizon, but from the outside, through a quantum process. Simplifying, the virtual pairs particle-antiparticle are separated, so that one of them falls in the black hole, the other escapes. So the virtual pair becomes real, but without violating the energy conservation, If you account for the potential energy of the particles, the black hole looses weight, although it swallowed a particle. Hawking calculated that after a long time, black holes evaporate and eventually explode. So what's happening with all the information which fell into the black hole and reached the singularity? Will it be recovered, or is it lost forever? If it is lost, then this raises some problems to the physics, especially to the unitary evolution, which is very important for quantum mechanics. This is the puzzle. If it is not lost, then how can it escape? You can read more about this in Hawking's "A brief history of time", but since then, many new things were understood. You may find interesting the links in the
Wikipedia article. As you may have seen from my previous comment, my viewpoint is that the Einstein equations can be reformulated so that they can be continued through the singularities, and nothing is in fact lost. Many people don't like this, because they want to promote their new theories by saying that general relativity fails because of the singularities. But one should not confound general relativity with our limited understanding of general relativity, because it is in fact the latter which fails.
Best regards,
Cristi
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Congratulations Christie with your latest works. I understand that you make singulairities workable with SR. You use a lot of mathematics that I cannot follow, but thet is not the problem, I was thinking that singulairities are only a mathematical way of expressing a non existing entity, in mathematics we can count with it but in "reality" that is materialistically limited they just cannot "exist" (also with the BB), so in my opinion (maybe wrong) mathematics can not always explain "reality". It is our mind ,consciousness that can easily think about infinities, singulairities the root of -1 etc. This of course is a great gift and indicates that there is more ...
think free (sorry Steve)
Wilhelmus
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Cristi Stoica replied on Mar. 20, 2012 @ 19:22 GMT
Dear Wilhelmus,
Interesting thoughts on existence and mathematics. Well, I don't see any contradiction in the existence of singularities in the real world, but I can't say if they really exist or not. Since our limited understanding of mathematics grows permanently, I also cannot say if there are regions of reality which mathematics will never be able to describe. Maybe there are, or maybe not.
Best regards,
Cristi
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Steve Dufourny replied on Mar. 20, 2012 @ 23:21 GMT
Hi Christi,
I see the singularities like the ultim informations.
So they exist indeed and they are inside the physicality at these planck walls if I can say.
The works of Hawking are relevant about the emissions, that said I don't agree about the explosion and evaporations. The Spheres, central to galaxies have proporties and rules.But I don't see why they shall disappear. In fact when we extrapolate mathematically a serie like an evolutive BH for example, so we must insert limits about the equilibriums between mass.
So in your line of reasoning, you are right because the ultim informations(main central sphere, the biggest volume) are conserved like the entropy.So Hawking has just forgotten these limits in the calculations of the serie of evolution with the correlated mass.
That said I d like insist on the fact that we cannot analyze beyond these singularities , because we are beyond the physicality.These singularities are just at these walls separating the unknown and this physicality. So why beyond Christi ? The best analyzes are when they take into account the rationalism and the determinism of this physicality, this 3D universal sphere and its cosmological and quantum spheres.So why beyond the walls of these particules or why beyond our Universal sphere and its limits.You know if the physicality exists, there are reasons. The secerats are inside this physicality, at these walls and we are very far at this moment.We cannot see these singularities , these ultim codes. It is like desiring seeing the central spheres of the quantum world and for the cosmological world and the central universal sphere of the universal sphere in evolution. We cannot see these codes at this moment.But we can see the steps before...
I beleive strongly Christi that the codes are precise about the general evolution, so I don't see a necessity for a degenerescence of BH.
the mass curves space GR and the light speed is constant SR .I see the relativity just like this.
Regards
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Steve Dufourny replied on Mar. 20, 2012 @ 23:27 GMT
you are comic Whilhelmus :) don't say sorry, you are free you know to say what you want. I am free to critic like I want also :)
peace my friend.:)
ps the -, the 0, the infinities must be analyzed with the biggest rationality. In fact it exists a lot of laws about these meanings. Do you know the alephs of Cantor ? The - and the 0 in fact do not really exist, and the infinity also. But we can class them and utilize them also like tools.
Regards
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Lawrence B. Crowell replied on Mar. 22, 2012 @ 02:54 GMT
I was planning to write about one of your papers here and this general blog entry. However, it is getting a bit too late. I have been working on similar extensions, but with the intention of looking at singularities as dual to the holographic horizon.
Cheers LC
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Cristi Stoica replied on Mar. 22, 2012 @ 19:17 GMT
Hi Lawrence,
Thank you for your interest, I would like to hear your viewpoint.
Best regards,
Cristi
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Steve Dufourny replied on Mar. 22, 2012 @ 21:24 GMT
Hi Lawrence, me also I d like hear your point of vue, I am sad that one of 2 mavericks is not with us.
Regards
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Lawrence B. Crowell replied on Mar. 23, 2012 @ 01:59 GMT
Cristi,
The extensions you are making are analytic. In this must then be some aspect of complex variable. What I can’t help but think is there is some underlying quantum mechanical aspect to this. The quantization of singularities is necessary in order to determine if there is some dualism between the QFT configuration of the stretched horizon in holography and the field state of the singularity. So I have been playing around with similar ideas in order to generalize the Hawking radiation theory.
I am again posting late and do not have quite the energy to type out a lot of stuff. I will maybe try to write something here that is longer this weekend. The analytic smoothing of physical singularity in a black hole provides a way in which post selected states due to Hawking radiation can demolish states on the stretched horizon which correspond to the pre-selected states. If there is a duality then this should mean the quantum information which enters the BH is encrypted in another form as the post selected states. This follows the weak measurement approach to quantum mechanics by Ahrahonov and Vaidman.
Steve,
It is too bad about Ray Munroe. He was to say the least adventurist about all of this, where I am a bit more cautious. Some of his work on the 5-fold symmetries I did with him, and we published a paper together. He was a few years older than me, but not by too much. I had a friend a few years ago die of a heart attack as well. I had a full check up last year and everything checked out alright. I hope it stays that way.
Cheers LC
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Cristi Stoica replied on Mar. 23, 2012 @ 07:57 GMT
Hi Lawrence,
Interesting observations.
Indeed, if the fields can evolve through the singularity, the unitarity is restored. Interesting the explanation with pre-selected and post-selected states.
I discussed a few months ago with a physicist the possibility of counting the states of the singularities to account for the entropy of the black hole, but I did not advance yet in this direction. My hope is that this will follow from some global conditions, because locally they seem not to be present. Speaking of the duality you mention between singularities and horizon, I see it somehow analogous to the duality between a field and its source, which appears to be a singularity of the field. My view on the stretched horizon is somehow different than Susskind's, in that I don't think it is in conformity with the principle of equivalence to have a special stretched horizon, on which special things happen. But the holographic principle I think doesn't need a fixed stretched horizon. I think there is more freedom, like as we choose a closed surface in Gauss's law for the electric field (to continue the analogy with the duality field-singularity).
For the moment, I concentrate in pushing the classical GR to understand better what happens at singularities. My guess is that here there are some hints regarding quantum gravity.
Best regards,
Cristi Stoica
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Steve Dufourny replied on Mar. 23, 2012 @ 15:17 GMT
Hi Lawrence, Christi,
Take care Lawrence.
About the singularities and the unitarity, it is intresting to see how the pure mecanical and thermodynamical laws are conserved.
Regards
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Lawrence B. Crowell replied on Mar. 24, 2012 @ 02:10 GMT
You do have to read Susskind’s book on the holographic principle. He does say at the end there is a bit of a problem with resolving the issue of the singularity and what happens there. I think there is a duality between the data on a stretched horizon and the singularity. I think this might have to do with the conformal symmetry flow of how symmetries on certain scales are buried on other scales. This is an aspect os Zamalodichov’s renormaliaztion group flow.
LC
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Cristi Stoica replied on Mar. 24, 2012 @ 07:43 GMT
Hi Lawrence,
I did read it, and I think in the closing comments he doesn't mention the issue of singularities, but the issue that the BH entropy is each time calculated by a trick, and we don't have the understanding of the connection between entropy and area. This is in conformity with the point I expressed earlier. Susskind defines the stretched horizon as "a fictitious membrane at Planckian distance from the horizon", which does something strange to information: records and re-radiates it, and in the same time allows it to pass. I have to disagree with this, because it leads to contradictions (even if they are "unobservable contradictions"), and because violates the equivalence principle.
But, like I said, I agree with you that there is a connection between singularities and entropy. I think that this connection is direct, rather than via a "stretched horizon". Unless instead of the stretched horizon we consider an equivalence class, something like a homology class. I hope I will return in a few months with a more precise description of what I said.
Best regards,
Cristi Stoica
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Lawrence B. Crowell replied on Mar. 24, 2012 @ 15:06 GMT
The last paragraph Susskind talks about the infalling observer who crosses the horizon as a “big hole.” So he is talking about the interior in general, but of course that includes the singularity.
Your insight on a homology I think is right on. I attach a paper I got published a couple of months ago. This involves the counting of states on a black hole horizon. I have been working on how these states are dual to interior states according to elliptic curve cohomology.
Cheers LC
attachments:
Crowell_EJTP_counting_states_in_ST.pdf
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Cristi Stoica replied on Mar. 24, 2012 @ 17:06 GMT
Lawrence, thanks for the attachment. Now I think it is more clear to me what you meant.
Cristi
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Steve Dufourny replied on May. 7, 2012 @ 12:08 GMT
Christi,
I forgot this thread.
Well , about the BH ? I must insist on the fact that it is a sphere with a mass, a volume, rotations, rules, propoerties....if they are black, they are reasons considering the relativity and the light and its 3D perception. Like a person who has studied a lot about the sigularities and this entropy.I suppose that you insert limits in your domains. The duality is rational. Not need of paradoxal extrapolation loosing their foundamentals.
These BH have emissions and absorptions. They sort and synchronize like all spheres.If you say that nothing can escape, you are false.Perhaps the Hawking Radiations can help when we insert relativistic domains. The aim is not to add the ideas but to understand the generality Christi.
If people wants to understand what is the entropy and its distribution by the singularities and its codes. So the roads, deterministic must be inserted !!!
The rest is vain after all.
spherically yours and in 3D !!!
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Steve Dufourny replied on May. 10, 2012 @ 11:19 GMT
Christi,Lawrence, I become completely crazzy you know.My paranoia and my headackes are numerous. I have meds but I become crazzy.
ps I ask me if the spheres of a galaxy at the cosmological scale are correlated with the quantum spheres of this cosmological system.The singularities and the entropy are correlated also with the planck walls.
Probably that each galaxy possesses each own quantum entanglement. It is relevant considering the volumes and the rotations, if the number of the serie of uniquity is considered with the biggest rationalism. The proprotions can be analyzed.
The volumes and mainly the main central spheres, are at the wall and possesses the entropy by combinations mass/light. If each galaxy possesses its own spherical volumes. So the quantum entanglement in its pure finite serie is correlated inside the specific galaxy and its own entanglement also.
The claculation of the central volumes and the central main universal volume can be made with relevance. The princimple of equivalence.....
Regards
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