# Black hole inhibitors

1. Jun 8, 2008

### jonmtkisco

1. As a thought experiment, imagine a region of space which (inexplicably) is very densely filled with electrons and contains no other matter. Gravity would drive collapse towards a singularity, but electromagnetism would cause the electrons to repulse each other. Since electromagnetic potential is far stronger than gravitational potential per unit of mass, is it impossible for such a collection of electrons to self-collapse into a black hole, regardless of the density of the electron cloud? My guess is that it is impossible.

2. Now let's imagine a region of space filled very densely with (electrically neutral) dust. Gravity causes the dust cloud to collapse, but then random motions and interactions. cause the dust cloud to virialize. If dust continues to infall into this region (from "outside"), thereby increasing its density indefinitely, and the newly infalling dust also virializes, is there any density threshhold at which the total gravity of dust would "overcome" the virial resistance and cause the cloud to collapse into a black hole? (No gravity waves or external perturbations are allowed in this exercise). My guess is that the dust cloud would continue to virialize more and more with ever increasing angular momentum, withstanding collapse until the virial motion reaches a significant percentage of the speed of light, at which time the energy required to further increase the angular momentum would grow (due to special relativity) to the point where the cloud collapses into a black hole rather than gaining further angular momentum.

Jon

2. Jun 8, 2008

### Wallace

You are describing the formation of stars, i.e. overdense regions that collapse as far as the physics of the material making up the overdensity permits. Your questions would be answered by any text dealing with stars, their formation evolution and death.

3. Jun 8, 2008

### jonmtkisco

Hi Wallace,
There is no such thing as a star formed entirely of electron plasma, with no ions.

And my virial question is addressing a scenario where the dust density is far higher than in the molecular clouds where "natural" stars form.

In both cases, I'm trying to explore what would happen in an artificially created extreme environment.

Jon

Last edited: Jun 8, 2008
4. Jun 8, 2008

### Wallace

As stars collapse the density becomes large, and further collapse is prevented by the physics of the material of the cloud. This is no different in the situation you describe. Your dust cloud would either form a star, black hole or whatever depending on the mass of the cloud and the elements it is composed of in exactly the same way as standard star formation.

As for the electron only case clearly the electrostatic repulsion would prevent collapse up until the mass was large enough to overcome the electron degeneracy pressure. Look up the Chandresarkar limit, again from any text about stars.

5. Jun 8, 2008

### jonmtkisco

Hi Wallace,

The Chandresarkar limit applies to electron degenerency, when electrons are confined so tightly that they impinge upon the Pauli Exclusion principle.

However, I do not believe that a cloud comprised entirely of electron plasma could ever compress itself gravitationally to the Chandresarkar limit. Total gravity increases as the mass of the plasma increases, but the electrostatic repulsion of the negatively charged plasma also increases in the same proportion. Thus I think that in principle it is impossible for gravity alone to ever collapse an electron plasma.

Regarding the ability of virial motion to stop gravitational collapse, I think that as the total mass is increased, the virial motion will be radiated away as heat, which will tend to diminish any subsequent increase in angular motion. However, if additional density is added at a fast enough rate, there may be insufficient time for the cloud to radiate away much virial energy. For that reason, it seems to me that angular motion could continue to increase. When the temperature gets hot enough, nuclear fusion will kick in to add outward pressure. If we continue to add dust mass rapidly, the gas pressure will be overcome and electron degeneracy and then neutron degeneracy will occur. If more mass is added, the structure would collapse to a black hole. But we have not dealt with the possibility that the structure will continue to add virial angular motion which could prevent (not merely reduce) further collapse. As I said, my guess is that in this scenario the only thing which could prevent the angular motion from increasing indefinitely is special relativity as the rotating dust particles approach the speed of light.

Jon

Last edited: Jun 8, 2008
6. Jun 8, 2008

### Wallace

Again, this is all dealt with in standard texts on star formation. I strongly recommend that you look to read up on this if you are interested in this further.

7. Jun 8, 2008

### jonmtkisco

Hi Wallace,

I think you already know there is no standard text on star formation that discusses the gravitational collapse of clouds comprised solely of electron plasma. That scenario does not occur naturally.

And I have yet to find one that describes a situation where a virialized dust cloud far denser than any natural molecular cloud collapses directly into a black hole.

I would greatly appreciate if you would direct me to a specific text reference, but only if it deals with the specific scenarios I mentioned. Frankly I don't think you can because I believe such a text does not exist. But I am happy to be proved wrong because I want to learn about this subject.

Jon

8. Jun 8, 2008

### Wallace

The 'specific scenario' you describe is no different to parts of the process of star formation. I'm not sure why you think it is any different? You've got a dense lump of stuff in which gravity is (or isn't) balanced by thermal or other sources of pressure. Such objects are called stars. Calling it 'a virilised dust cloud' doesn't change the physics, and the physics that matters is the same as what occurs in stars.

Neutron stars are pretty dense objects, and if you go much denser then you get a black hole. What happens to your dust cloud will depend on its density in a way no different to stars.

9. Jun 8, 2008

### jonmtkisco

Hi Wallace,

I recognize that the virialized dust scenario is not entirely different from standard star formation. However, I'm posing a scenario where both the dust density and total mass are so extremely high that the dust cloud collapses gravitationally straight through the star phase and into the degenerate matter phases. My specific question is at what point the virial angular velocity reaches a maximum, and what specifically prevents it from increasing beyond that maximum? I suppose that if nothing else happens first, eventually the dust particles will be pressed tightly together, and at that point surface friction should prevent individual particles from gaining individual virial motion. But presumably the dominant collective virial angular momentum would be transferred to the resulting solid lump. Then will the lump continue gaining rotational angular momentum as it further collapses, or is this the end of that process?

The electron plasma scenario departs much further from any natural scenario, since as far as I know there is no known situation in which vast freestanding clouds of pure electron plasma would form naturally. My only point here is that, regardless of how much total mass increases, the electron plasma will never collapse gravitationally at all, not to the form of a star or a solid, and certainly not to the Chandresarkar limit. In this kind of scenario, electrostatic repulsion will always prevail over gravity, and the cloud must inevitably disperse.

Jon

Last edited: Jun 8, 2008
10. Jun 9, 2008

### hellfire

I think that for point 1 you are not right and the cloud should collapse into a black hole.

Consider the usual collapse steps or levels in stars. At every of the levels you have some fermions that determine a degeneracy pressure. If gravity overcomes the degeneracy pressure, the fermions become compressed too much for the exclusion principle to hold. Then, nature solves the problem by converting those fermions into other ones with a higher degeneracy pressure. This process takes place until there is no fermion anymore to convert to. Then a black hole is formed.

For the usual star scenarios with baryonic matter the last step would be some kind of quark star. If gravity is still stronger quarks will be futher compressed. To avoid a violation of the exclusion principle something must occur. Since quarks are elementary particles and since no other reaction is possible, a black hole is formed.

I would then conclude that for a cloud of elementary fermions (electrons or whatever) a black hole would be formed if gravity is strong enough.

Last edited: Jun 9, 2008
11. Jun 9, 2008

### stevebd1

I think what jonmtkisco is saying is that the inverse beta-decay process which allows the transition from electron-degenerate to neutron-degenerate matter wouldn't be an option if all particles where electrons (no protons to capture the electrons, hence no neutrons for neutron-degenerate matter) which implies that electron-degeneracy would prevail regardless of the pressure/densities brought on by the gravitational collapse. Maybe, under extreme conditions, if the inverse beta-decay option isn't available, the electrons would form tauons and then a whole new form of degenerate matter with a new process of collapse but the end result still being a black hole (a negatively charged Newman one at that)? Speculative but I suspect that a group of electrons with a mass in excess of 3+ sol could not undergo gravitational collapse without becoming something exotic.

12. Jun 9, 2008

### jonmtkisco

stevebd1, your description of my point is correct. There can be no neutron degeneracy if there are no protons for the electrons to mate with!

More fundamentally, I don't see how an electron plasma could collapse even the slightest amount, let alone to the point of inverse beta-decay. The strong electrostatic repulsion would cause the cloud to spontaneously disperse from the very start.

Here's an esoteric question: Why is the Pauli Exclusion Principle not considered to be a fifth "fundamental force", along with the strong and weak nuclear forces, gravity and electromagnetism? It's not a manifestation of any of the four forces. Maybe effects can be characterized as forces only if they have an "attraction" component, which Pauli doesn't have (?)

Jon

Last edited: Jun 9, 2008
13. Jun 9, 2008

### jonmtkisco

Here's a related question about virialization:

Galaxies tend to virialize extensively, with only a small percentage of their baryonic matter condensing in the center (as a supermassive black hole). On the other hand, stars tend to virialize very little, with only a tiny percentage of their matter avoiding collapse into the center (forming the star). Why the difference?

Superficially, one might expect a galaxy to be more prone to extensive central collapse, due to the huge gravity well caused by its dark matter halo. Stars on the other hand do not seem to have dark matter halos.

If stars virialized as much as galaxies do, we'd be hearing about star-mass "dust devils" that look like miniature galaxies. But of course we don't.

Does the difference between galaxies and stars result from the sheer scale difference between them, the different collapse durations, the different angular momenta, or perhaps the different particle sizes?

Jon

Last edited: Jun 9, 2008
14. Jun 9, 2008

### NYSportsguy

Damn you guys are hella smart. Can any one of you explain String theory to me?

15. Jun 9, 2008

### jonmtkisco

Hi NYSportsguy,
I can't. String theory makes no sense to me so I mostly ignore it.

Jon

16. Jun 9, 2008

### Quisquis

I'm stepping pretty far out of what I actually know here, but I would speculate that it has to do with the large amount of dark matter that appears present in galaxies. If you consider the http://en.wikipedia.org/wiki/Galaxy_rotation_problem" [Broken], you could conclude that what's keeping all that mass from infalling is the same thing that's keeping the rotation curve from falling off as expected.

Following from that it would make sense that it would not occur on the star formation level because there is no large amount of dark matter at the edges of our solar system to counteract the natural gravitational attraction.

Last edited by a moderator: May 3, 2017
17. Jun 9, 2008

### jonmtkisco

Hi quisquis,
That's an interesting idea, but I do not think it's the explanation. The Newtonian Shell Theorem says that if matter is distributed spherically around a centerpoint, the shells of matter outside of the object in question have no gravitational effect on the object. Thus only the matter (both dark and baryonic) which is closer to the center than the object would affect it, and the resulting gravity would be entirely inwards towards the center.

I found a recent star formation paper http://arxiv.org/PS_cache/astro-ph/pdf/0604/0604615v1.pdf" [Broken] which may shed some light on my question. It says that virial velocities caused by turbulence in a molecular cloud tend to increase with scale, following the formula:

(well my laTex isn't working, but the formula is:) v is equiv to R^1/2

If that formula holds up to the very large scales of galaxies, it would be easy to see why they have more virial angular momentum and thus are less prone to collapse to the center.

Jon

Last edited by a moderator: May 3, 2017
18. Jun 10, 2008

### hellfire

jonmtkisco, how do you explain the formation of a black hole from the collapse of a neutron star or a quark star? The same mechanism would apply for your electron cloud.

Last edited: Jun 10, 2008
19. Jun 10, 2008

### NYSportsguy

Jonmtkisco -

My professor at Stanford was one of the founders of String theory.

I know it has something to do with linking quantum field theory and general relativity equations on a sub-atomic scale.

20. Jun 10, 2008

### jonmtkisco

Hi Hellfire,

Here's how Wikipedia describes collapse of a neutron star into a black hole (bold added):
One would need to examine the TOV equation and the Equation of State (which is poorly understood) to try to figure out how much degeneracy pressure a pure degenerate neutron gas produces to resist further compression.

On the other hand, I assume that a pure degenerate electron gas also has an equation of state which would further resist compression after the Pauli Exclusion Principle has been completely overcome. I have no idea whether it has a "stiffer" or "softer" equation of state, more or less resistant to compression, than a degenerate neutron gas. I haven't seen anything written on this specific subject, e.g. no electron equivalent to the TOV equation. (To be clear, I'm not talking about the Chandrasarkar limit, because that's the stage where electrons combine with protons, and as we've said this scenario includes no protons.)

Certainly there is some mass and density limit beyond which a degenerate electron plasma could be externally forced to collapse into a black hole. One can readily imagine a scenario where the electron plasma is entirely enclosed within a dense spherical shell of electrically neutral matter, and this outer shell supplies enough gravity to collapse the whole structure into a black hole.

In any event, as I said I think the most important point here is that a pure electron plasma is entirely incapable of compressing itself to the point of testing the Pauli Exclusion Principle, because the strong electrostatic self-repulsion should avoid ANY initial gravitational collapse.

Jon

21. Jun 10, 2008

### jonmtkisco

Now that LaTex is back, the formula is:

$$v \propto R^{1/2}$$

(I meant "proportional to" when I said "equivalent to").

So anyway, I guess the best technique to utilize virial motion to prevent collapse into a black hole is to start with a supersized and superdense dust cloud. Galaxy scale is better than star scale, and galaxy cluster scale is even better. I surmise that at these larger scales, virial motion is defeated slowly over time only by random collisions (and near-collisions) between stars, and by the perturbative influence of gravity waves. What I don't know is how dense a galaxy cluster must become in order to spontaneously collapse almost 100% of its matter into a black hole within a reasonable timeframe, say 20 million years. There is no indication that such high densities occur naturally.

Jon

Last edited by a moderator: May 3, 2017
22. Jun 10, 2008

### Haelfix

Jon. It does not matter if there are only electrons present. If you have an overdense clump of them (say you prepared it somehow), they will undergo the exact same stellar formation process as any other lump of matter.

The only difference is they will have a lower mass threshold (TOV limit) to form a bh than say a bunch of protons, since they will not phase transition into a neutron degeneracy state and instead promptly become a bh.. Also they carry extra EM energy, so that will further reduce the threshold if you properly take GR into account.

What is true (at least I think), is that no such object can ever exist naturally (barring something extreme), since one of the simple assumptions of stellar formation is isotropy of the dust. The electrons will never form an overdense system.

23. Jun 10, 2008

### jonmtkisco

Hi Haelfix,

1. Why will an electron plasma have a lower mass threshold to form a black hole? Don't they still have a resistance to quantum degeneracy? In other words, even if the electrons are pushed tightly together, won't they still will resist being further crushed into an amorphous blob? Just as neutrons do.

2. You say that the electromagnetic energy carried by electrons causes them to have higher gravity per unit mass than, say, neutrons or protons?

3. Of course I agree that a "large" electron plasma cloud is not a natural occurrence in nature. I said that in my first post. My point is that if one could be artificially created (not farfetched) it would never self-collapse at all. True or false?

Jon

Last edited: Jun 10, 2008
24. Jun 10, 2008

### Haelfix

Gah reply was eaten.. Semi brief version
1) If there are only electrons present by hypothesis, they have no parameter space known in current physics with which to fall back on, since they are stable fundamental particles. Since they cannot undergo inverse beta decay (as with regular dust) they will presumably form a BH right at the Chandreskhar limit (the cutoff equilibrium point between electron degeneracy pressure and gravitational forces), and not at the TOV limit.

2) I wouldnt put it that way, since protons also carry charge. However there is not necessarily the same EM stress energy content, since there are global EM fields present in the electron case. I do not know if this is significant or not to effect things that much in the hydrodynamic equations typical of stellar collapse models or not, but I think maybe yes.

3) False. Although amusingly it occurs to me that to even bring an electron plasma into a small enough volume with sufficient mass would require a ton of work. You would probably collapse yourself into a bh, long before you would reach the desired configuration.

25. Jun 10, 2008