Primordial Black Hole as nucleus for gravitic atom

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I'd like to consider a primordial black hole in the absence of Hawking radiation.
When you consider the case of a primordial black hole with a Schwarzchild radius on the same order as the radius of a proton, I calculate its mass to be at around 6.75x10^11 Kg. If I then calculate the gravitational force this PBH would exert on, say, a neutron sitting at about the same distance as the ground state orbital radius of a Hydrogen atom's electron, I come up with 2.69x10^-5 N. This is greater than the electostatic binding force that a Hydrogen nucleus exerts on its electron at this distance. Considering this fact, I can imagine such a PBH acquiring bound particles until it becomes the seed of a macroscopic object, since unlike a normal atom that stops acquiring electrons once it becomes electrically neutral, the gravitational force the PBH exerts would only be diminished by distance.

First question: Since Hawking Radiation is theoretical, would this be the expected behavior of a primordial black hole if it turns out that Hawking radiation doesn't exist?

Second question: I understand the basic mechanism of Hawking radiation. But why wouldn't particles produced by the Hawking radiation mechanism become gravitational bound, since the binding force would seem to be at least a strong as the electrostatic force that holds atoms together? Is there some reason that all such particles are extremely energetic?
 

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  • #2
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Hi Matmos, you're bringing up really interesting questions.

First question: Since Hawking Radiation is theoretical, would this be the expected behavior of a primordial black hole if it turns out that Hawking radiation doesn't exist?
First, while hawking radiation *is* theoretical, it is pretty well established (and analogous phenomenon have recently been observed).
If hawking radiation doesn't exist, however, I still don't think this is what would happen. There would be no forces or properties of the BH to keep the system stable (analogous to the exclusion principle and strong-forces in atoms)---i.e. the BH would simple accrete matter instead of forming stable systems.

why wouldn't particles produced by the Hawking radiation mechanism become gravitational bound, since the binding force would seem to be at least a strong as the electrostatic force that holds atoms together?
Hawking Radiation is a fundamentally statistical process. The only particles which are emitted as radiation are those that happen to have high enough energy to escape. The reason why hawking radiation is so weak, is that there is only a small range of viable energies for this to happen. The vast-vast majority of virtual-particles forming near the event horizon ARE simply bound, and are thus uninteresting.
 
  • #3
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Thanks so much for your response!

I've done a bit more research into the derivation of Hawking radiation, and so I accept your answer to my second question. I'd dispute your characterization of gravitationally bound Hawking particles as "uninteresting" (The idea of particles having gravitationally determined energy orbitals and releasing quanta of gravitational energy as they transitioned from one orbital to another interests me...how could such quanta be detected? etc), but I can see how even initially bound Hawking particles would just get blasted away by the energetic Hawking radiation.

But your answer to my First question leaves me confused. Not the part about Hawking radiation being well established and accepted, but the part about it being unstable without the presence of forces analogous to those of a normal atom such as strong nuclear forces and the exclusion principle. I wasn't aware that the strong nuclear force played any role in determining the shape or stability of electron orbitals. And I don't see that the exclusion principle would be absent here...at least as applied to interactions between bound particles.
It does occur to me that there is a small but non-zero probability of 'finding' the particle within the event horizon. I suppose this means all bound particles would eventually vanish within? But since the volume is very very small compared to the volume of the orbital I've described, wouldn't it take a very long time for this to occur? Would the average time of "disappearance" be measured in microseconds, days, years?
 
  • #4
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I'd dispute your characterization of gravitationally bound Hawking particles as "uninteresting"
If they're bound, they don't become 'real,' they stay virtual and thus have no effect---which Is what I meant by 'uninteresting.' You're right, I could have come up with a better term :)

I wasn't aware that the strong nuclear force played any role in determining the shape or stability of electron orbitals.
It doesn't really, but it does allow neutrons and protons to form stable nuclei.

And I don't see that the exclusion principle would be absent here...at least as applied to interactions between bound particles.
If, somehow, electrons were momentarily able to stably orbit a micro BH, they wouldn't be degenerate as their energies are so high. Also, even if they *were* degenerate, degeneracy pressure would be insufficient to prevent gravitational collapse, as these electrons would be highly relativistic.
 
  • #5
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"If they're bound, they don't become 'real,' they stay virtual and thus have no effect---which Is what I meant by 'uninteresting.' You're right, I could have come up with a better term :)"

Sounds like we're not talking about the same thing. If a pair of virtual particles appears, and one strays over the event horizon, while the other does not, the remaining particle becomes "real". This "real" particle may be outside the event horizon but still lack the energy to escape the conventional gravitational binding force. These are the ones I find interesting.

"It doesn't really, but it does allow neutrons and protons to form stable nuclei."

I was considering how the PBH would be the analog of a normal atom...with the PBH taking the place of the nucleus, and the force of gravity replacing the electrostatic force as it acted on, not just electrons, but any particle with mass in its vicinity. I'm not sure how forming stable nuclei would play a role in determining whether the orbits of such particles would be stably bound.

"If, somehow, electrons were momentarily able to stably orbit a micro BH, they wouldn't be degenerate as their energies are so high. Also, even if they *were* degenerate, degeneracy pressure would be insufficient to prevent gravitational collapse, as these electrons would be highly relativistic."

Remember, we're now considering micro black holes in the absence of Hawking radiation. Is there some other reason that such bound particles would necessarily have highly relativistic energies?
 
  • #6
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I think to talk about the nucleus of the atom being a BH puts you on fairly dodgy ground as neutrons and protons are pretty much well established, you'd probably be better off saying that fundamental particles such as quarks and electrons might be PBH's but even then I'd tread carefully as there's a lot of information to take into account that can't necessarily be explained by basic BH mechanics. For the record, you don't necessarily have to write off Hawking radiation, HR actually reduces for a BH when you take into account spin (a) and charge (Q) though the black hole would have to be close (if not exactly) maximal where a/M=1 or Q/M=1 or even a^2+Q^2=M^2 though this is meant to be in conflict with BH thermodynamics.
 
  • #7
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I am not in any way suggesting that the nucleus of an atom is a BH. Nor would I care to speculate as to whether quarks or electrons might be PBHs. My reference to a "gravitic atom" was an attempt to provide an analogy only for illustrative purposes. I guess it's done the opposite.
I was simply pointing out that in the absence of Hawking radiation, a micro black hole would seem to acquire bound particles in stable orbitals via the force of gravity. Typically people brush off the notion of gravity stably binding subatomic particles together because it is by far the weakest of the forces. But in the case of a pbh, there seems to be enough mass to overcome this weakness.
 
  • #9
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Considering this fact, I can imagine such a PBH acquiring bound particles until it becomes the seed of a macroscopic object, since unlike a normal atom that stops acquiring electrons once it becomes electrically neutral, the gravitational force the PBH exerts would only be diminished by distance.
The problem with this idea is that unlike an atom, the matter in the ground state of the PBH will fall into the BH. Once matter from the ground state falls into the BH, that opens up an energy state for new matter to come in.

A better example of a "gravitic nuclei" is a neutron star or white dwarf.

Also one of the more interesting arguments that I've seen that "dark matter" can't be neutrinos is this. You imagine a galaxy as a giant atom, and the count the number of possible energy states for that giant atom. You can show that if all of those energy states were filled with neutrinos, that there still would not be enough mass to account for dark matter.

One other thing is that there is no reason that you need a PBH to make a gravitic atom. Any bit of matter would do.

First question: Since Hawking Radiation is theoretical, would this be the expected behavior of a primordial black hole if it turns out that Hawking radiation doesn't exist?
If Hawking radiation doesn't exist then we have big, big problems. One thing about Hawking's argument is that you can show that if Hawking radiation doesn't exist, then you can build a perpetual motion machine with a black hole in the middle. Something that sucks up heat without getting warm itself causes a *lot* of problems with thermodynamics.

The reason that Hawking's work is really interesting is that he combines gravity, quantum mechanics, and thermodynamics in interesting ways, and there are several independent reasons why you have to have Hawking radiation.

But why wouldn't particles produced by the Hawking radiation mechanism become gravitational bound, since the binding force would seem to be at least a strong as the electrostatic force that holds atoms together?
Gravity is very weak and electrostatic forces are very strong.
 
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  • #10
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Just click the link I gave to the technology review article. It explains it more clearly.
 
  • #11
First question: Since Hawking radiation is theoretical, would this be the expected behavior of a primordial black hole if it turns out that Hawking radiation doesn't exist?

Second question: I understand the basic mechanism of Hawking radiation. But why wouldn't particles produced by the Hawking radiation mechanism become gravitational bound, since the binding force would seem to be at least a strong as the electrostatic force that holds atoms together? Is there some reason that all such particles are extremely energetic?
The relevant equations are in the arxiv http://arxiv.org/pdf/1105.0265v1" that the blog references (some of which seem to be fairly straightforward analogues of the schrödinger equation with the coulomb potential (i.e., just exchanging 1/4πεo for G and square of the electron charge with the masses of the PBH and electron)).

According to the wikipedia article on http://en.wikipedia.org/wiki/Hawking_radiation" [Broken] the energy radiated is defined to be that measured at infinity, so Hawking radiation is necessarily (gravitationally) unbound (at least the part that contributes to the temperature of the object measured by distant observers).
 
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  • #12
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So Hawking radiation solves a thermodynamic contradiction posed by black holes, and if the particles produced are gravitationally bound (even though they've escaped the event horizon), they no longer serve that purpose? OK. I probably should have left that question out of this topic and just focused on the behavior of a pbh in the absence of Hawking radiation.

These guys have come up with an electromagnetic 'signature' to look for when these GEA's ("Gravitationally Equivalent Atoms" as they call them) pass through the earth and get their captured orbital matter stripped away. It sounds like Hawking radiation is so firmly grounded in theory that there will be much head scratching if such signatures are found.
But then again, these GEA's might provide a likely culprit for dark matter and the inexplicably rapid cosmological structure formation (at least it was still unexplained when I took my Cosmology class long long ago).
Long odds perhaps, but it would be an exciting find.
 

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