Smallest stable black-holes

[Hasanuddin]

What is the smallest sized possible black-hole? And what are the implications of the answer to this question?

According to cosmologic observation, the smallest black-hole ever viewed from Earth is roughly 3.8 solar masses. SPACE.com -- Smallest Black Hole Found

However this observation does not establish the lower limit to achieve a stable black-hole. For one thing, that structure has been growing ever since its creation and is observed growing today. For another, there are several different models that do seem to suggest the lower limit of stability for a black-hole to be much smaller than 3.8 solar masses.

I posit this discussion not out of pure whimsy. The deductive Dominium analysis, on which I am working, asserts that in the primordial Universe, long before CMB, mini black-holes were formed near the centers of each galaxy. Those of a similar type to the galaxy itself (matter in the case of the Milky Way) went on to form the central AGN, while opposite-type MBH (antimatter for the Milky Way) either were trapped in the MAC structure or were ejected and are now recorded as “dark-matter.”
http://hypography.com/forums/alterna...anuddin-8.html
http://hypography.com/forums/alterna...tml#post264943
Unfortunately, the Dominium model is deductive, therefore it is only useful in supplying the big-picture narrative, but is unable to supply numeric specifics, such as the exact lower limit of the mass needed to achieve MBH stability. Hence I am quite interested how folks of this forum can weigh in and explain nuances of different arguments that are floating out there.

Specifically, of theories that do use numeric methods, there appears to be both agreement in general terms, but disagreement on specifics. It appears that all theories concur that MBH can be stable for all sizes larger than one Plank mass, which is about 2.0e−8 kg or 1.2e19 GeV/c2.. Micro black hole - Wikipedia, the free encyclopedia However, there appears to be disagreement for masses below this. There are some who believe that special conditions might cause black-hole production at lower masses.
[hep-ph/0106219] High Energy Colliders as Black Hole Factories: The End of Short Distance Physics
[hep-ph/0106295] Black Holes at the LHC
The case for mini black holes - CERN Courier

Although, the common understanding is that below one Plank mass, MBH will evaporate away; this belief is not assumed by all. [gr-qc/0304042] Do black holes radiate?

Most recently, there are even those who have asserted that MBH could be much more stable than originally assumed [0901.2948] On the Possibility of Catastrophic Black Hole Growth in the Warped Brane-World Scenario at the LHC

So the question is: which is it & why? What is the smallest size for a black-hole to stably exist? And what are the implications of this debate?

[Moontanman]

It's my understanding of black holes that none of them are stable long term. All black holes eventually evaporate, even the super massive black holes will evaporate given enough time. One thing I have asked about at one time or another is this. Would a back hole made of antimatter behave compared to a matter black hole and what would happen if a matter black hole and an antimatter black hole were to merge, assuming both were of equal mass would they cancel out?

[CraigD]

Originally Posted by Hasanuddin

What is the smallest sized possible black-hole?

Assuming that the quantum mechanical prediction of Hawking radiation is correct, the lifetime of a black hole into which no matter or EM radiation is infalling is exactly proportional to the cube of its mass. Specifically:



With this, and reasonable assumptions about typical rates of radiation and infalling matter, you can calculate the mass of a black hole of various short lifetimes. For example, a kg black hole has a lifetime of about 1 second, a kg one about 1 year, and a kg one about s, about the current age of the universe according to Big Bang model. By way of comparison, kg is just a bit more than the mass of a large artificial structure like the Three Gorges Dam.

In principle, a small black hole could be stable – that is, be at equilibrium, neither gaining nor losing mass – if the power of its infalling matter and radiation equals that of its Hawking radiation. For the cosmic background radiation – which all objects are more or less guaranteed to receive – a black hole of about kg – about the mass of Earth’s moon has about this equilibrium.

In principle, an arbitrarily small black hole could be stable if it received a arbitrarily large amount of EM radiation (infalling matter couldn’t be used to stabilize an arbitrarily small black hole, because the exclusion principle limits the amount of fermionic mater that can occupy a given volume of space.)

Even though the first of these scenarios is easily imaginable, neither has been observed, nor is a compelling scenario that could result in either occurring been described in any literature of which I’m acquainted.

Originally Posted by Hasanuddin

And what are the implications of the answer to this question?

[Boerseun]

Originally Posted by Moontanman

One thing I have asked about at one time or another is this. Would a back hole made of antimatter behave compared to a matter black hole and what would happen if a matter black hole and an antimatter black hole were to merge, assuming both were of equal mass would they cancel out?

I have never actually thought about this!

Matter and anti-matter is supposed to annihilate each other 100%, leaving only a flash of gamma rays in its wake. But consider two black holes of equal mass, one matter and the other anti-matter. If they fall together, would the gamma burst be able to escape?

I suppose so - cause the matter constituting the mass on both black holes would now be gone through annihilation, and there won't be anything left of the black holes, so there won't be an event horizon on either side or in total - there would be just one goddamn big gamma burst and zero black hole! And anything that was orbiting the black holes would just carry on in a straight line seeing as the gravity is now gone all of a sudden - assuming they'd survive the gamma flash...

It's a strange, strange universe, this. But in an infinite universe, if this haven't happened yet, it sure will, sometime in the distant future...

[Boerseun]

...having read my above post, I guess a better question would be what would happen if two black holes fell together, one matter, the other anti-matter, but the difference between the two is still big enough to cause a black hole?

Say the minimum mass for a black hole is x. Say the matter black hole's mass is 4x, and the mass of the anti-matter black hole is x. Would the infalling anti-matter black hole cause any gamma radiation to escape? Keeping in mind that the anti-matter black hole will have to pass well beyond the matter black hole's event horizon before touching any matter, I don't think so... But the event horizon should suddenly and quite dramatically shrink upon annihilation?

Curious...

Very curious...

[Jay-qu]

Originally Posted by Boerseun

...having read my above post, I guess a better question would be what would happen if two black holes fell together, one matter, the other anti-matter, but the difference between the two is still big enough to cause a black hole?

Say the minimum mass for a black hole is x. Say the matter black hole's mass is 4x, and the mass of the anti-matter black hole is x. Would the infalling anti-matter black hole cause any gamma radiation to escape? Keeping in mind that the anti-matter black hole will have to pass well beyond the matter black hole's event horizon before touching any matter, I don't think so... But the event horizon should suddenly and quite dramatically shrink upon annihilation?

Curious...

Very curious...

Well B, have you heard of the saying 'Black holes have no hair'? Black holes are only thought to carry a few basic properties: mass, charge and entropy. From this understanding it seems that the 'information' of the matter being either matter or antimatter is lost. Thus the black holes would simply collide and make an even larger black hole. This is what you may expect to happen, after all a matter/antimatter annihilation produces photons that could not escape from the black hole.

[Moontanman]

If indeed hassanuddins ideas about matter and antimatter are true then there should be some serious consequences if such different black holes were forced together.

[Hasanuddin]

Good I am glad that there are some good answers and considerations. I’ll reply in two sections because there appears to be two sub-threads.

As to the primary question of the smallest size that a black-hole can be and exist stably.

Originally Posted by CraigD

For example, a 2e5 kg black hole has a lifetime of about 1 second, a 7e5 kg one about 1 year, and a 1e11 kg one about 1.4e10 s, about the current age of the universe according to Big Bang model. By way of comparison, 1e11 kg is just a bit more than the mass of a large artificial structure like the Three Gorges Dam.

Okay, let me just clarify… you are talking about only the evaporating side of the equation… correct?

What about the other side of the dynamic? Consumption. Does a black-hole consume more when the density of compactable material is high? Deductively the answer must be, “Yes.” If a black-hole is in a pure vacuum then nothing could be consumed. As material is added to the surrounding matrix rates of consumption necessarily increase. Although there may be a maximum rate of consumption under a given set of conditions, altering such conditions, e.g., increasing pressure, could result in increased consumption rates. All this is important to the original question, because by increasing the rates of assimilation/accretion you could reach the dynamics necessary for stability at lower and lower masses.

This point loops back to your post when it is said

Originally Posted by CraigD

In principle, a small black hole could be stable – that is, be at equilibrium, neither gaining nor losing mass – if the power of its infalling matter and radiation equals that of its Hawking radiation. For the cosmic background radiation – which all objects are more or less guaranteed to receive – a black hole of about 4e22 kg – about the mass of Earth’s moon has about this equilibrium.

Perhaps I am misreading you, but it appears that you are saying that equilibrium for a black-hole only assimilating/accreting the energy from the CMB, but nothing else, will be stable at a mass of 4e22 kg. Am I reading you correctly? So, a smaller, yet still stable black-hole could be achieved under conditions where more energy/mass are being accreted. Is that correct?

To this line of inquiry, CraigD did appear to address these queries,

Originally Posted by CraigD

(infalling matter couldn’t be used to stabilize an arbitrarily small black hole, because the exclusion principle limits the amount of fermionic mater that can occupy a given volume of space.)

The problem is, following the link provided offers no evidence to support the notion that infalling energy would be interchangeable infalling mass to achieve black-hole stability. After all doesn’t the famous equation E=mc2 suggest an interchangeability between mass and energy? Nowhere on the link discussing the Pauli Exclusion Principle is it suggested that E=mc2 does not apply.

[Hasanuddin]

The question of antimatter black-holes is a truly intriguing question… and one to which I have applied quite a deal of thought to over the past couple years.

First, I believe that no matter which theory one refers to there is indication, on a fundamental level, that anti-matter black-holes (AMBH) are theoretically predicted. Most would agree that antimatter is supposed to be the mirror particle of matter. Assuming parity and symmetry, one would assume that all functions possible in a matter-based system should be possible in an antimatter-based system, e.g., anti-fusion, anti-biochem, and therefore anti-matter black-hole formation.

Now, the dynamic of AMBH depends fundamentally on which arbitrary hypothesis you favor: Dominium’s gravitational-repulsion or popular-bias’ universal-attraction. Depending which model one subscribes to, the resulting expected dynamic of AMBH is radically different.

Gravitational-repulsion: Up side… under this scenario AMBH would be a substance that would highly repel any all mass. Think about it: this could be a propellant to end all future searches for propellants. It could easily be an inexhaustible “fuel,” by securing it in a “cage with a window” mass entering tangentially to the window could be accelerated out of the spacecraft at a extremely high velocities, thereby achieving extremely high accelerations.

Originally Posted by Boerseun

But consider two black holes of equal mass, one matter and the other anti-matter. If they fall together, …

No need to continue this thought on this post or continuing on to the next post. Under conditions of the Dominium hypothesis, the gravitational repulsion between AMBH and a matter-based black-hole would be so great that it would be impossible for them ever to collide. Actually, within the Dominium model, the only time that AMBH and matter-based black-holes collide together was during past and future Big Bangs.

Down sides… Cost, though that would be expected to decrease with anticipated higher efficiencies. Cage and storage technologies do not yet exist. Though the processes seem intuitively plausible.

Universal-attraction: Up side… High energy source. If matter and antimatter gravitationally attract then they would be expected to collide. There is no reason to suggest that principles of annihilation altered. Therefore any surrounding matter that it accidentally accretes would result in an annihilation event. Whether the gamma photon created would have sufficient energy to leave the remnant black-hole is another question.

Neutral… Then there is the notion that under conditions of universal-attraction matter black-holes and antimatter black-holes will attract and annihilate with one another. The problem with this supposition is that despite the billions of viewable galaxies, stars, and etc, this type of interaction has never been hinted at.

Down side… Again, same as the Dominium cost and storage.

True under either scenario
Because of the highly dense nature of black-holes, the concentrated matter would take up little space.

[Jay-qu]

Antimatter does not have anti-mass, it will act gravitationally just like any normal matter. Therefore I would not expect an AMBH to be repulsive.

You may find reading on white holes interesting Hasanuddin.