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Group discussion > Black Hole Atom
Black Hole Atom
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Dyau
447 days ago |
Friends, let me share a problem I've been pondering.
Consider two black holes which we define as below:
1) Black Hole 1 (BH1) has the mass of a proton (0.938 GeV) and contains a positive charge equivalent to the charge of a proton (1.602176487 × 10e−19 coulombs).
2) BH2 has the mass of an electron (511 eV) and contains a negative charge equivalent to the charge of an electron.
We can easily show that these two particles can be brought together to form a stable quantum-mechanical bound state. Since the bound state is stable, the black holes within it should not decay due to Hawking radiation. This is in essence a stable black hole atom.
Can such a bound state be formed? What would be the properties of such a particle? Would love to hear your ideas/thoughts/comments!
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Daniel
447 days ago |
wait... if you consider those Black Holes based only on General Relativity, how can you link it with a quantum mechanical description for a bound state?
Sorry if I'm deviating from your main idea, but I couldn't even figure out the situation...
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Dyau
447 days ago |
You are right, we cannot quantize the system if we consider BHs based on GR.
Here I'm not considering BHs based on GR. I am describing a gedanken (thought) experiment:
- We take two Schwarzschild Micro BHs - MBH1 (mass: 0.938 GeV, charge: proton charge) and MBH2 (mass: 511 eV, charge: electron charge) and place them in close proximity in a box.
- The two MBHs should them form a stable quantum mechanical bound state whose properties can easily be defined using the good old Schrodinger equation.
My argument is that since the bound state is perfectly stable, the MBHs within it will not decay due to Hawking Radiation.
My questions are:
- Can such a bound state be formed?
- What would be the properties of such a particle?
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Daniel
447 days ago |
Let's suppose that's possible. Looking at the ground state of this bound state, from what we know of Quantum Mechanics, there's a non-zero probability of finding the "electron BH" in the center of the system. It seems we get into a paradox, for the center is the "proton BH". What would it mean "a non-zero probability to find the eBH inside the event horizon of the pBH"?
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Dyau
447 days ago |
You are absolutely right, there's a non-zero probability of finding the eBH in the center of the system. Yes, it could be interpreted as a paradox.
However, this is then also true of the regular, non-black hole hydrogen atom; that there's a non-zero probability of finding the electron in the center of the system where the proton should be.
The resolution of this apparent paradox is as follows:
- The system is a center-of-mass system: both the eBH and pBH revolve around the common center of mass.
- The eBH may sometimes be found at the physical center of the system; and so may the pBH. However this does not mean that both are simultaneously present at the center of the system. The exclusion principle prevents from happening in the H atom.
We need to study the properties of the BH atom bound state to understand what happens in this case. Do the two BHs overlap physically? If yes, they will coalesce and the bound state will be destroyed. If no, then the bound state is stable and may have interesting properties.
What are your thoughts?
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Daniel
447 days ago |
But that's a main difference from the usual Hydrogen atom from that BH Atom. Even though the eBH and the pBH do not share the same space, that doesn't mean the uncairtanty principle is beyond the Schwarzchield radius. Diferent from the e and p, a black hole has a related "size", that's the Schwarzchild radius. so that "center of system paradox" gets more complicated, at least that's what I think...
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Dirk Banks
447 days ago |
Interesting discussion.
At a first glance, I'd say it should be possible to create such a bound state in suitable conditions.
A stable bound state of black holes? It should have the properties that we associate with SHDM.
I remember seeing a paper by a couple of Indian guys about BH bound states. The idea certainly is plausible.
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Dyau
447 days ago |
I agree, Daniel. This problem is much more complicated than it seems at face value. However, like Dirk mentioned, I believe such bound states are possible and can "throw light" upon Dark Matter :)
I'm trying to persuade our friend Ragav to work on this problem. Hey Ragav, where are you? :)
Dirk, I've seen the papers you're referring to. They call these bound states "holeums". The papers are available on the Arxiv - search for holeum.
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Dyau
447 days ago |
I'm signing off until evening - got to go to the university! See y'all later.
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Ragav
447 days ago |
here i am Dyau....first things first-i sincerely appreciate the coceptual hold of our two other mutual friends here-Daniel and Dirk. So with Dyau, this is a beautiful "Triple D bound state" huh?!?
now,my views on Daniel's arguments about the non-zero probability is that-quantum mechanically,there is always a finite probability of finding the eBH or pBH anywhere within the bounded system. We can normalize the probability to any arbirary area,WITHIN the diameter of the BHatom.
now,this is not as straight forward as it appears-because,the most important thing here is to calculate "HOW NEAR/FAR CAN THE TWO BLACK HOLES GET??". do their vicinities allow their event horizons to overlap?let's clarify that point first! the rest pretty much follows,i guess.
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editor
447 days ago |
You can't have a proton black hole.
The Planck mass is 1.539 x 10^-8 kg which is about 10^19 proton equivalents.
The smallest BH you can have is Planck mass and 10^35m in diameter.
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Dyau
446 days ago |
Well all I can say is that this is a matter of conjecture. There is one school of thought that says that the Planck mass is the lower limit of mass, while there is another that says one can have sub-Planck masses. Some people believe that sub-Planck mass particles (Planckons/Cornucopions) should be considered to be stable elementary particles. There is no consensus on this, and no evidence of the veracity of eiter of these hypotheses.
Until we have iron-clad evidence one way or the other, I believe that we can safely use sub-Planck mass particles in theories. It's better to formulate a (possibly) incorrect theory than to not explore that direction at all.
What are your thoughts on this?
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Dyau
446 days ago |
See my latest bookmark. I had no idea that someone has worked on this problem! I need to study this!
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Daniel
446 days ago |
So far in that article I've read that he considers mini-BHs forming bound-states with "regular" matter. But that is surely important to know, perhaps even before considering a miniBH-miniBH atom. Will try to read it also, at least the main parts.
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Dyau
446 days ago |
Yes indeed, they have considered bound states of charged black holes with "regular" matter. The concept can be applied to BH-BH bound states too, though. Will be interesting if someone has worked on that.
Still going through the paper ...
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Ragav
435 days ago |
Hey guys,it suddenly occured to me that what if the laws of physics at the sub planck domain were a little different from the ones at the planck or the higher domains?!? like as in, suppose certain chaotic and non linear aspects dominate the sub-planck scale, so much so that the laws pf physics at such minute scales does not fall into the desciption of the ordinary quantum mechanical description at all?!?
would it be a testimony to the fact that "history repeats", beacuse we witnessed a similar discrepancy (and a gap) when we made a transition from classical to the quantum!??!
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Dyau
431 days ago |
Ragav, you've hit the nail on the head. QM and physics as we know it are expected to break down when we cross the sub-planck threshold. At least, this what the majority of physicists believe.
Let's take Hawking Radiation as an example, which is a semi-classical theory that involves quantum tunneling. Black holes emit HR at a rate given by
dm/dt = -k/m^2
where m is the black hole mass and k is a constant. A glance at this equation is enough to understand why large black holes are more or less stable and why micro black holes are expected to expire in a spectacular explosion.
This law may not be valid at a sub-planck mass scale. It is possible that the decay process of sub-planck mass black holes is "democratic" in nature, that is, they may exhibit varying decay behavior. There even is speculation that such black holes may not decay at all.
So yes, there could be a discrepancy and a gap when we finally make the transition and develop a theory of sub-planck physics.
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Ragav
429 days ago |
Hey Dyau, thanks for your encouraging and supporting remarks....it also occured to me that we can go about trying to look at the problem taking the "ensemble approach".... let me substantiate the view:
as we know, the dynamics of Balck holes is studied on the basis of statistical arguments, like the Hawking law of black hole thermomodynamics or the Hawking-Bekenstein temperature etc: so instead of taking purely deterministic apporach to MBHs, why not take a statistical one?!? one could for example, borrow the concept of radioactive half-life or the "rate of decay of an ensemble of MBHs"!!! that way, we eliminate any discrepancies of absoluteness....not to mention the miniscule sub planck scale where the slightest fluctuations tend to perturb the system greatly! what say people?!?
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Dyau
428 days ago |
I can't help agreeing with you! A statistical approach to the problem of sub-planck MBH behavior will average out their "democratic" behavior. One could certainly come up with the rate of decay of an ensemble of MBHs. However, the study of a MBH population will throw up other insteresting problems: what about the reabsorption of Hawking radiation in the MBH population? That will certainly bring the decay rate down. It will depend on several factors, primary among which will be the MBH density. Throw in some background blackbody radiation, and we're talking about an early-universe simulation! That's my kind of physics!
Know what Ragav, you should take up one of these problems and crack it. You have all the right ideas.
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debasish borah
340 days ago |
Dyau commented "I agree, Daniel. This problem is much more complicated than it seems at face value. However, like Dirk mentioned, I believe such bound states are possible and can "throw light" upon Dark Matter :)"
I have a doubt. Even if such a bound state is formed out of eBH and pBH , will it be stable considering the fact that eBH and pBH will radiate HR (unlike our normal e and p)? And since they have tiny masses, they should radiate fast. But dark matter particles should be long lived to give rise to the observed abundance.
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Dyau
340 days ago |
Very good question, Debashish. A black hole emits Hawking Radiation at a rate inversely proportional to the square of its mass. Consequently, tiny BHs such as our eBH and pBH should undergo near-instantaneous evaporation - if they are isolated.
It is very important to emphasize the condition of isolation.
A black hole in a box (lab) that contains vacuum is isolated. A black hole immersed in a radiation field is not isolated, neither is a black hole that is part of a population of black holes whose number density is large enough for them to reabsorb each other’s Hawking radiation. Consequently, a black hole lying in inter-stellar space cannot be considered to be isolated as it is immersed in the CMBR field, however weak it may be; and can also absorb inter-stellar gas and other material. Similarly, a black hole that is part of a bound state is not isolated.
It is instructive to note that in nature, a free neutron decays but a neutron in a stable nucleus does not. The rule of thumb here is: unstable particles do not decay when they are part of a stable bound state. By "stable", I mean quantum-mechanically stable.
What are your views on this?
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debasish borah
340 days ago |
Your point seems convincing. A neutron decays via weak interaction, however inside a nucleus strong interaction dominates and hence neutron remains stable. Similarly in an atom formed by eBH and pBH, electromagnetic force has to dominate over gravitational force so as to prevent eBH and pBH from decaying by emitting HR..is it correct?
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Dyau
338 days ago |
That's an interesting way of looking at it.
So what you're saying is that since the weak interaction is ~ 10^6 times weaker than the strong interaction, effects caused by it should be suppressed within a bound state domainated by the strong interaction.
If we follow that line of thought, the gravitational effects caused by the masses of eBH and pBH will be suppressed by the electromagnetic force which dominates the bound state.
But what if eBH and pBH were not charged? What if we consider a purely gravitational bound state consisting of two micro black holes of equal mass?
The answer is: it will still be stable. The reason for this is that Hawking radiation is not a gravitational phenomenon. It is caused by field effects. Let me explain the mechanism in brief:
According to quantum field theory, there is no such thing as “nothing”. Vacuum itself has an underlying background energy that exists even in space devoid of matter. Virtual particle – antiparticle pairs are constantly created and annihilated in vacuum. These virtual particles exist for a limited time and space, introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty Principle. They are “temporary” in the sense that they appear in calculations, but are not detectable as single particles due to their very brief existence. Indeed, they are detectable only as forces. The existence of these particles is no fiction. Though they cannot be directly observed, the effects they create are quite real.
Consider a virtual particle – antiparticle pair that is created right at the edge of a black hole’s event horizon. Usually, such a virtual pair will self-annihilate almost instantaneously. However in this case, there is a finite probability that one of the particles will cross the event horizon and disappear into the black hole. If this happens, the other particle/antiparticle will escape from the black hole. Conservation of energy requires that the particle that fell into the black hole must have had a negative energy. The black hole thus foots the bill of the escaped particle: it loses an amount of mass-energy equivalent to that of the escaped particle.
To a user at a distance, it will appear that the black hole is radiating a steady stream of particles and antiparticles; and is shrinking over time.
The rigorous theory of the mechanism of Hawking radiation involves quantum tunneling, which we need not discuss here. What needs to be understood is that only isolated black holes can undergo HR. Black holes which are part of a bound state are not isolated, and therefore won't decay.
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debasish borah
338 days ago |
Thank you very much Dyau...I had the misconception in my mind that HR is purely a gravitational effect. Things are clear now. Thus we can have a stable bound state out of eBH and pBH. Although this bound state won't emit any HR, can each one of eBH and pBH drag any matter around them towards them? I just want to knw like you said only isolated BH can undergo HR, is it also true that only isolated BH can drag matter around them towards itself?
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debasish borah
336 days ago |
I don't think I was very clear about my last post. I think although its true that only isolated BH can radiate HR, its not true that only isolated BH can pull matter around it to itself. Otherwise there won't be any difference between a bound state formed out of two ordinary e and p and a bound state of eBH and pBH. Thus although a bound state of eBH, pBH does not emit HR, it should behave like a gravitational singularity, right?
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Dyau
336 days ago |
You are mostly correct here Debasish. However, there is a caveat here.
One must not look upon a bound state as two particles moving together; rather, one must see a bound state as an intrinsic particle itself. Thus, it is the combined mass of the bound state that gravitates and pulls matter to itself, rather than the individual BHs that form the bound state.
Whether the bound state of eBH and pBH will behave like a gravitational singularity depends on only one factor - the radius of the bound state - which is determined by solving the Schrodinger/KG equation for the system. If the radius of the bound state is smaller than its Schwarzschild radius, then the bound state itself is a black hole, and it will emit HR. On the other hand, if its radius is greater than its Schwarzschild radius, it will behave as an ordinary particle.
One must realize here that if you can show that such a bound state exists (whose radius is smaller than its Schwarzschild radius), it will be a clear case of a black hole having internal structure - which is one of the holy grails of black hole physics.
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debasish borah
335 days ago |
Thanx once again Dyau. This seems really interesting. Even if such bound state do not form a BH which emit HR, we can still study it from dark matter point of view. So there are plenty of motivations for studying these things carefully.
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debasish borah
328 days ago |
Thank you very much. Can you please also suggest some reference where work is done on isolated black holes and hawking radiation etc?
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debasish borah
322 days ago |
oh I have found some other papers of L.K. Chavda regarding bound state from primordial BH...Actually one of my prof was of the opinion that BHs (in a bound state) will also emit HR and an asymptotic observer will still be able to detect the HR. Now I have got enough references to show her that it is not true always. ..:)
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Dyau
319 days ago |
Hey Debasish, sorry for my late reply. I am away as I have the 'flu.
Yes, the two papers I mentioned describe various PBH bound states. It is clear from Chavda's paper that these bound states will be perfectly stable. You've got enough ammo for your prof! :)
You may also want to see the Custódio and Horvath papers, they deal with black hole evolution and Hawking Radiation. I'm giving the links to three, there are more. Search on SPIRES/Arxiv for the remainder.
http://arxiv.org/abs/gr-qc/0203031
http://arxiv.org/abs/gr-qc/0302079
http://www.sbfisica.org.br/bjp/files/v35_1210.pdf
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debasish borah
319 days ago |
Oh I am sorry to hear that. I hope everything is fine now. Anyway thanks a lot for the references. :)
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