What does the equation C = 12 J mean for black holes?

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Summary:
Saw this formula on documentary about black holes. What does it mean … really mean ... in lay terms as much as possible.
Just saw a documentary about resolving Hawking's "information paradox". In my own lay terms the physicists appear to theorize resolving the paradox with with their proposed C = 12 J . C is the central charge (which I don't fully understand) and J is the total angular momentum of the black hole. 12 is an interesting and elegant coefficient (IMHO) having something to do with geometry, vectors and spheres … perhaps

In lay terms, the physicists seem to be saying that this simple formula demonstrates that the event horizon (EH) of a black hole has the capacity to absorb and retain information about all matter and energy that has fallen into the black hole by means of holding or releasing the information somehow through a quantum mechanism or structure called "soft hair" that radiates information out and away from the EH. Thus the information paradox could be resolved if C = 12 J is valid.

My question(s) are how does some value for total angular momentum relate to a capacity for a black hole system (through its soft hair) to preserve information? What is the central charge (in simple terms) in this context? Why 12 ??
 

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  • #2
anorlunda
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Summary:: Saw this formula on documentary about black holes. What does it mean … really mean ... in lay terms as much as possible.

Just saw a documentary about resolving Hawking's "information paradox".
Please provide a link to what you saw so that we know what you are asking about.
 
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The documentary's focus is more on the first image of a black hole in 2018 or so but delves into Hawking's work on the paradox up to his death. Here is documentary : https://www.netflix.com/title/81343342
 
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Hawking prompts his team (six months or so before his death) with "How many conformal killing vectors on the two sphere. An infinite number?" The team guesses at first (3)? Then (6) perhaps?

Hawking also asks "Would diffeomorphism give all the entropy?"
 
  • #5
Ibix
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I'm afraid that black hole thermodynamics is beyond me. I've suggested the thread be moved to the relativity forum where you may get more help. I have to warn you that I suspect that the answers will boil down to "you need to learn the maths for this to make any sense".

One thing I do know is that the angular momentum of the hole affects the area of its event horizon, and it's the event horizon area that's related to the entropy of the hole.
 
  • #6
Doc Al
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Here's the paper that explains how they derived that equation for central charges: Black Hole Entropy and Soft Hair

It's rather technical, so it may not help -- as @Ibix has warned. (I won't pretend to understand it.)
 
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Ibix
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I note that the paper comments that they choose to work in units where ##c=G=k=\hbar=1##, so in more usual unit systems that 12 is probably going to become ##12c^\alpha G^\beta k^\gamma \hbar^\delta## where the Greek symbols represent numbers chosen to make units consistent.
 
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  • #8
PeterDonis
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Just saw a documentary about resolving Hawking's "information paradox".
This would be better described as a proposed resolution. This entire area of research is purely theoretical; there is no way to do experiments to test any of the proposals. Partisans of various proposals like to claim that they are the final answer, but without experimental confirmation, such claims should be taken with a huge helping of salt.
 
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PeterDonis
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I've suggested the thread be moved to the relativity forum where you may get more help.
This is not really classical relativity; it's quantum gravity research. I have moved the thread to the Beyond the Standard Model forum.
 
  • #10
PeterDonis
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C = 12 J . C is the central charge
Actually, it's not, it's just a constant in the formula (called ##c_R## or ##c_L## in the paper @Doc Al linked to). A better representation of the full central charge would be the full coefficient in ##K_{m,n}## in that paper, which turns out to be ##J m^3##. The factor of ##12## only appears in the formulas ##c_R = 12 J## and ##c_L = 12 J## because a factor of ##1/12## appears in a previous formula for ##K_{m,n}##. So I'm not sure the factor of ##12## has any direct physical significance; the key result of physical significance seems to me to be the factor ##J m^3##.
 
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In Feynman style, might you be able to simplify for lay persons the general nature of this proposed resolution? Does it show, for example, some relationship between surface area of event horizon and entropy as Ibix suggests. Any other ways to help non-quantum physicists conceptualize this resolution would be appreciated.

Also, is it in any way legitimate to suggest that all matter falling into a black hole may essentially reach the speed of light with that matter becoming all kinetic energy with total of mc ⌃2 .
 
  • #12
Ibix
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Also, is it in any way legitimate to suggest that all matter falling into a black hole may essentially reach the speed of light with that matter becoming all kinetic energy with total of mc ⌃2 .
No, definitely not. Nothing with mass can reach the speed of light under any circumstances and it cannot "become kinetic energy". Energy is a property of a particle or field, not a thing, so "becoming kinetic energy" makes no sense, I'm afraid.
 
  • #13
anorlunda
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Any other ways to help non-quantum physicists conceptualize this resolution would be appreciated.

You might try this book by Leonard Susskind. It is written for laymen.
https://en.wikipedia.org/wiki/The_Black_Hole_War

If I remember correctly, it does discuss how the surface area of the event horizon is proportional to the information contend.

Susskind has gone beyond that now suggesting that information complexity theory might be use to unite quantum physics with general relativity. There are numerous videos of his lectures on YouTube. Search for "ER=EPR". But it is all cutting edge speculative research, not layman stuff.
 
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No, definitely not. Nothing with mass can reach the speed of light under any circumstances and it cannot "become kinetic energy". Energy is a property of a particle or field, not a thing, so "becoming kinetic energy" makes no sense, I'm afraid.
I've read recently some measurements or approximations have indicted that some black holes rotate at nearly the speed of light, they say for example NGC 1365 is turning at 84% the speed of light…. Thus it's reasonable to speculate that matter drawn into the hole does at least approach the speed of light and that much of the matter's inertial? mass would consist of kinetic energy — just a guess that's probably wrong. So if matter is not becoming energy (like kinetic energy) at least in part, what does the matter that "falls" into a black hole actually become?
 
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PeterDonis
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just a guess that's probably wrong
Please stop guessing. Personal speculation is off limits here at PF.

This topic is a very advanced one, and I have changed the level of the thread to "A". The paper itself is aimed at experts who have that level of background knowledge of the topic; you should not expect to be able to understand it if you don't have that background knowledge. I can't follow a lot of it myself since my knowledge of the subject area is pretty basic.

In Feynman style, might you be able to simplify for lay persons the general nature of this proposed resolution?
First you have to understand what they are trying to "resolve". They are not trying to "resolve" whether a black hole's entropy is proportional to the area of its horizon. That's already agreed on by everybody.

All they are trying to do is to see if they can get a particular kind of quantum gravity model they are interested in to predict that the entropy of a black hole is proportional to the area of its horizon. In other words, they are trying to see if this kind of model is a viable candidate for a quantum gravity model of a black hole. "Soft hair" is just a name for the particular quantum gravity degrees of freedom that this model is using.

how does some value for total angular momentum relate to a capacity for a black hole system (through its soft hair) to preserve information?
Because the total angular momentum (and the total mass) affects the area of the hole's horizon, which in turn is (proportional to) the hole's entropy. This is not anything particular to the model being investigated in the paper; it's a known property of black holes in classical General Relativity.

What is the central charge (in simple terms) in this context?
"Central charge" is a particular property that particular kinds of algebras have (the model in the paper is using a kind of algebra called a "Virasoro algebra"). I don't know of any simple way to explain it if you don't already have a good understanding of what algebras are, what kinds of algebras there are, and how their properties differ. Possibly other experts here can do a better job of that.
 
  • #16
Ibix
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Thus it's reasonable to speculate that matter drawn into the hole does at least approach the speed of light
There's no such thing as speed unless you specify speed relative to something, so you need to be rather careful how you think about it. That said, it's reasonable to suppose that matter orbiting a black hole might approach the speed of light in some sense - but it can never reach it.
much of the matter's inertial? mass would consist of kinetic energy — just a guess that's probably wrong.
Better to say that defining mass in general relativity is complicated. Inertial mass isn't a particularly helpful concept outside Newtonian physics, since the relationship between force and acceleration is more complex even for point particles.
So if matter is not becoming energy (like kinetic energy) at least in part, what does the matter that "falls" into a black hole actually become?
It doesn't become anything. It just falls in and hits the singularity. Classical general relativity doesn't know what happens there. Quantum gravity should have an answer but, as Peter notes there are a lot of theories and we don't know which one (if any) is right.
 

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