Black Hole Atom

Dyau:

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 :

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 :

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:

1. 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.
2. 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:

1. Can such a bound state be formed?
2. What would be the properties of such a particle?

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Daniel :

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 :

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:

1. The system is a center-of-mass system: both the eBH and pBH revolve around the common center of mass.
2. 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 :

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 :

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 :

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 :

I’m signing off until evening – got to go to the university! See y’all later.

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Ragav :

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 :

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 :

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?

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 :

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 :

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:

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 :

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 :

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 :

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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