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/alternative-theories/18910-the-dominium-model-by-hasanuddin-8.html

http://hypography.com/forums/alternative-theories/19536-the-dominium-model-part-2-a.html#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]

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:

 

[math]t_{\mbox{ev}} = \frac{5120\pi G^2M_0^{3}}{\hbar c^4}[/math]

 

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 [math]2 \times 10^5[/math] kg black hole has a lifetime of about 1 second, a [math]7 \times 10^5[/math] kg one about 1 year, and a [math]10^{11}[/math] kg one about [math]1.4 \times 10^{10}[/math] s, about the current age of the universe according to Big Bang model. By way of comparison, [math]10^{11}[/math] 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 [math]4 \times 10^{22}[/math] 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.

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

[Boerseun]

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]

...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.

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

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,

(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.

 

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.

[Boerseun]

Like Jay said, antimatter has exactly the same mass-gravity property as normal matter. Besides, if anti-matter were gravitationally repulsive, they would never fall together to fall a black hole in the first place.

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.

I'm not completely with you here. As far as I know, the only difference between matter and antimatter is that the charges are reversed. Electrons are positive in antimatter, and protons negative. If black holes only have mass, charge and entropy, then an antimatter black hole should be able to annihilate a matter black hole? Seeing as the only difference between the two is charge, and that's a property retained by a black hole?

 

So if they collide, first off the event horizons should merge around the common center of mass as the two approach, which should result in a (viewed from outside the common even horizon) mutual black hole with an even horizon looking more like a figure eight, or the infinity sign, which will again approach a sphere as the two meet up, upon which the even horizon would suddenly shrink as the mass is annihilated?

 

This is indeed very interesting, and definitely worthy of its own thread. (Sorry for thread-jackin', by the way)

[freeztar]

The question of AMBH vs. MBH annihilating was answered here by an Astronomer.

 

Curious About Astronomy: What happens when an antimatter black hole collides with a matter blackhole?

[Boerseun]

The question of AMBH vs. MBH annihilating was answered here by an Astronomer.

 

Curious About Astronomy: What happens when an antimatter black hole collides with a matter blackhole?

That guy said the same thing Jay said - also about the only things to be measured being just the mass, charge and angular momentum.

 

And my question remains the same - with the difference between matter and anti-matter merely being reversed charge, that is a property that will be retained by an anti-matter black hole?

[freeztar]

It would seem to me that a collision would cause anhilation which would produce lots of gamma rays. These gamma rays would be unable to escape and would be trapped. So, in essence, the resultant mass should simply be the mass of BH#1 plus BH#2. But that's just a guess.

[Boerseun]

This raises some awesome possibilities:

 

Say, for instance, the mass required for black hole formation is x. The MBH is 100x, and the AMBH is also 100x. Then the gamma burst would be trapped underneath the event horizon, until the resultant mass (after annihilation) reaches lower than that required for black hole formation, upon which all that gamma radiation would be released at once. That, ladies and gentlemen, would just be friggin' awesome...

 

You'd basically see a combined event horizon shrinking and shrinking and shrinking and then all hell breaks loose as the total energy of 200x is released at the same moment...

[modest]

This raises some awesome possibilities:

 

Say, for instance, the mass required for black hole formation is x. The MBH is 100x, and the AMBH is also 100x. Then the gamma burst would be trapped underneath the event horizon, until the resultant mass (after annihilation) reaches lower than that required for black hole formation

 

The photons that result from the annihilation have equal energy to the matter / antimatter before the annihilation. It's the energy which curves spacetime rather than just the rest mass and photons do have energy.

 

If you could enclose a hydrogen bomb in an impervious and infinitely strong box, the box would curve spacetime equally before and after the bomb in the box exploded. Before it exploded the box would contain mostly hydrogen and after the explosion it would have mostly photons, but the total energy of the box would be the same.

 

~modest

[Hasanuddin]

Hi folks,

 

A new thread has been started to address and discuss the nature of AMBH

...

 

I wholeheartedly agree with:

This is indeed very interesting, and definitely worthy of its own thread. (Sorry for thread-jackin', by the way)

I have no problem that several interesting lines of discussion have been opened. However, I want to stay focused (and I'm keenly interested in CraigD's response, and if anyone wishes to join the discussion of how/what could achieve the smallest stable black-hole.