Why spacetime quantization does not prevent blackhole formation?

[Andrea Panza]

Hi,
This is my first post and first of all I would like to thank all the contributors to this forum for the amazing amount of information provided here.
I’m not a physicist, but I like physics (although I have only a qualitative understanding of it) and I like to smash my brain on difficult and interesting subjects.
For what I understand some theories hypothesize that the space-time itself is not continuous but is quantized at the Planck scale. Thinking in terms of a quantized space I have problems to understand why black holes do actually exist. I’ll number the steps of my reasoning and I hope you can explain me where I’m wrong.
1. When a star is running out of fuel the energy output decreases and can’t counterbalance the gravity and the star starts to contract
2. The star density increases and if the star has sufficient mass, in its center the pressure will cause the density to rise over a critical value.
3. This critical value should be a Planck mass confined in a sphere with a radius equal to the Planck length: a ultramicroscopic black hole is born.
4. The birth of the black hole should cause a drop in pressure just around him since the event horizon is not a solid object and the matter will fall freely in it pulled by its own weight and by the fact that innermost layers of the nucleus will be accelerated more than the layers just above (spaghettification).
5. However even if in close proximity to the black hole the matter cannot fall in it at the speed of light (since matter cannot be accelerated to the speed of light).
6. But our original black hole has just the critical mass to start to exists and then will evaporate through awkings radiation before the surrounding matter should fall in it.
7. The heat emitted by the evaporating black hole should cause a shockwave compressing the surrounding (falling) matter and this, together with the weight of the above star layers should generate microscopic black holes of critical mass distributed on a spherical surface.
8. This balckholes should also evaporate before the falling mass from the above layers get in.

To me it is clear that the mass enters in the black hole increasing its stability before tha black hole evaporates, but I don’t understand how.
Do black holes evaporate through awking radiation only if surrounded by empty space? If the process is driven by virtual particles pairs I think (but maybe I’m really wrong) that the emergence of virtual particle pairs should happen in every point of the space (even the one with matter in it) not only in the vacuum.
Thank you in advance

Andrea

 

[Mordred]

You've posted quite a few questions some of the points I noticed are incorrect or not confirmed. Hawking radiation falls into both categories. Hawking radiation is an extremely slow process far slower than material can inrush. Any body can form a black hole if it collapses below its Shwartzchild radius even our own Sun. This doesn't occur except for larger solar masses I can't recall the exact value. Also if i recall correctly Hawking radiation won't start until its surrounding temperature drops below its blackbody temperature but I could be wrong on that last part.

I won't answer the portion on virtual particles as I don't understand it well enough even though I've read tons on the subject lol.
As far as the Planck length this is still a subject to be confirmed. equates to if space is bumby or smooth at small scales. Their have been various tests with certain frequencies of light from distance type 1a supernova that show that even on the Planck length scale vs frequency. Show indications of being smooth. So there is still some debate on the smallest unit possible in spacetime.

By the way welcome to the forum

 

[Mordred]

In the 1970s, Stephen Hawking showed that due to quantum-mechanical effects,
black holes actually emit radiation – they are not entirely black! The energy that
produces the radiation in the way described below comes from the mass of the
black hole. Consequently, the black hole gradually loses mass and, perhaps surprisingly,
the rate of radiation increases as the mass decreases, so the black hole
continues to radiate with increasing intensity losing mass as it does so until it
finally evaporates.
The theory describing why this happens is highly complex and results from the
quantum mechanical concept of virtual particles – mass and energy can arise
spontaneously provided they disappear again very quickly and so do not violate
the Heisenberg Uncertainty Principle. In what are called vacuum fluctuations,
a particle and an antiparticle can appear out of nowhere, exist for a very short
time, and then annihilate each other. Should this happen very close to the event
of a black hole, it can sometimes happen that one particle falls across the horizon,
while the other escapes. The particle that escapes carries energy away from the
black hole and can, in principle, be detected so that it appears as if the black hole
was emitting particles.
Black holes can be said to have an effective temperature, and unless this is less
than the temperature of the universe the black hole cannot evaporate. This temperature
is now ∼2.7 K – the remnant of the radiation left over from the Big Bang
which will be discussed in Chapter 9 – and is vastly higher than the effective temperatures
of even solar mass black holes. Eventually, in aeons, when the temperature
of this relict radiation has fallen sufficiently and assuming Hawking’s theory
is correct, stellar mass black holes may finally begin to evaporate – on a timescale
of 10^100 years!

This is cut and paste from " Introduction to Astronomy and Cosmology " by Ian Morison

 

[phinds]

...
Black holes can be said to have an effective temperature, and unless this is less
than the temperature of the universe the black hole cannot evaporate.

That has been discussed here several times and you are incorrect. What is confusing you is that the NET radiation will be inwards unless the BH temp is above the outside temp (which is as you say ∼2.7 K). That is, the BH both emits and absorbs radiation but it emits less than it absorbs. That is NOT the same as "it does not radiate".

 

[Mordred]

Fair enough I can relate to that. One of the hassles of taking things too literally regardless of source lol. That does help me a bit on another manual I'm studying in regards to Unruh effect, blackbody radiation and Hawking radiation.

 

[marcus]

Andrea, it's a clever objection to the formation of BH. In fact very small BH do explode with intense radiation very quickly as they come to end of life.

(According to Hawking semiclassical model.)

And if they start out very small, then the end of life would come quickly.

This is according to Hawking's formulas for the temperature and evaporation rate. but they are not based on a full quantum gravity theory. I think Hawking's model is only applicable to larger BH.

I don't think we have adequately addressed your paradox. We didn't say where your idea fails.

I think the answer is that when a dead star collapses to BH you do NOT get a single tiny one first at the very center.

Large black holes require less density. So you never have to reach the critical density for small BH formation. A whole big load of mass reaches ITS threshold density first, and SLURP presto you have a large BH. And they do not evaporate quickly.

So the mechanism you are proposing is clever---for Nature to avoid making BH by direct conversion (at the very center) of mass into Hawking radiation energy---but it does not work. Maybe somebody else can explain this better. There are probably several reasons it does not work. which you knew already---you were posing a paradox.

In Italy Andrea is a guy's name. (But not in Usa.) Welcome. It would be nice of you to say which so we do not get confused about him/her pronouns.

 

[Andrea Panza]

Hi Mordred,
Thank you for your answer(s), unfortunately I didn't explain myself properly and I made my question unclear.
I know that stars with 4> solar masses collapse in black holes, but my question was more or less like this:

under the hypothesis of a quantized space-time how is it possible that macroscopic BH do actually form?

Hawking evaporation is an extremely slow process for macroscopic BH, but the smaller is the BH the higher is its temperature. So the smallest possible BH should radiate at the highest possible temperature for the awkings radiation, having a radiating net emission as soon as they are formed (since everything around them has a lower temperature) and evaporating so fast that if space-time is quantized nothing could have time to fall in them to make them more massive and more stable.

 

[marcus]

Hawking evaporation is an extremely slow process for macroscopic BH, but the smaller is the BH the higher is its temperature. So the smallest possible BH should radiate at the highest possible temperature for the awkings radiation, having a radiating net emission as soon as they are formed (since everything around them has a lower temperature) and evaporating so fast that if space-time is quantized nothing could have time to fall in them to make them more massive and more stable.

That is all correct. But the collapsing core of a star does not provide the necessary conditions for microscopic BH to form. Larger BH can form already at LOWER DENSITY than is needed for microscopic BH to form. You can discover this by simple arithmetic. Please ask questions if you do not see why it is true.

In a stellar collapse, the density never gets high enough for microscopic (i.e. very low mass) BH to form. I explained this earlier.

 

[Andrea Panza]

Thank you Marcus,
Indeed I'm an Italian guy.
In truth I didn't want to formulate a paradox. I just wanted to understand where my reasoning was wrong. Thank you for explaining me about the different density requirements, I knew that the bigger the black hole the lower its mean density gets, but I didn't think about variable density requirements for BH formation. Do you have some reference I could read?

 

[marcus]

... variable density requirements for BH formation. Do you have some reference I could read?

Unfortunately I don't have a reference handy to mind, Andrea. There may be someone else who has one ready.

A simple explanation would go like this: a black hole (i.e. a BH event horizon) forms in non-expanding space when you have a mass M which is contained within its Schw. radius 2GM/c².

For M = solar mass that works out to R = 3 kilometers.

But a solar mass contained in a sphere of radius 3 kilometers is NOT VERY DENSE compared with Planck density. It is way, way less dense.

So when the core of a dead star is collapsing, the core just has to reach the density needed for a stellar mass BH way, way earlier. So that is what forms. The microscopic very hot tiny BH never has a chance to form because the density never gets in the right ballpark for it to form!

I realize this is a handwaving loosey-goosey explanation---it's intuitive for me and I hope can serve as explanation until someone else comes up with an authoritative reference, or themselves writes out the equations.

 

[marcus]

Since you say you are an Italian guy I will type for you from memory a bit of verse that I love in Italian and which you surely learned by heart in school:

Frati, io dissi, che per cento miglia
perigli, siete giunti al Occidente,
a questo tanto picciola vigilia

dei nostri sensi ch è del rimanente
NON VOGLIATE NEGAR L'ESPERIENZA (this is the spirit of empiricism)
di retro al sol, del mondo sanza gente (this is what physics and cosmology are about)

Considerate la vostra semenza,
fatti non foste a viver come brutti,
ma per seguir virtute e conoscenza.

Brothers, I shouted, who have had the will
to come thru danger and have reached the West,
our time awake is brief from now until

the senses die, and so I say we TEST
the sun's own motion and do not forego
the WORLDS BEYOND, unknown and people-less.

Consider the roots from which you sprang, and show
that you are human, not unconscious brutes,
but made to follow virtue, and to KNOW.

 

[Andrea Panza]

My dear Marcus,
a second passion of mine is Dante! I read and studied the Divine Comedy in italian, and I always thought that would have been extremely difficult have a translation able to both maintain Dante's poetic-phylosophical wiew and musicality, but this quote from odysseus is perfect also in english.

by the way, quoting Dante seems very appropriate on this forum since every part of the divine comedy ends with the word 'Stars'.

Literature aside I'm afraid I have another question for you ;)

Since the larger is the amount of matter, the lower is the density required to form a black hole if we find the average density of the universe now, we should be able to calculate which volume of space with such density could spontaneously form a ultrabig verly low density black hole right?
It could be possible to determine if we are inside such a big black hole?

 

[marcus]

...

A simple explanation would go like this: a black hole (i.e. a BH event horizon) forms in non-expanding space when you have a mass M which is contained within its Schw. radius 2GM/c².
...

the pattern of expanding distances is very interesting. In General Relativity, geometry has a life of its own. You could almost say that processes of geometric change have a kind of momentum. Once expansion has been initiated it wants to continue (of its own accord without anything forcing it to continue) and it will only gradually slow down or gradually speed up in response to other factors.

Distances beyond galactic scale tend to increase by a small fraction of a percent---at present it is 1/139 of one percent per million years. These largescale distances increase more or less uniformly without anybody going anywhere. It does not involve anyone approaching a destination---in this sense it is dynamic geometry and not like ordinary motion.

Because of this small percentage increase, the very great distances (that you would need as Radii to include enough matter to collapse, if the expansion could be halted somehow) are increasing on the order of the speed of light.

It is not a favorable condition for the formation of a BH.

Distances to remote galaxies are increasing faster than light. In order to make a BH it would first be necessary, by some bizarre mechanism which I cannot imagine, to STOP the expansion of the cosmic geometry.

I am glad you like Dante. He had many good ideas---and having the two travelers finally come up to the surface (at the end of the journey thru the Inferno) and see the stars was one of those good ideas. It consoles the heart and clears the mind to see the stars.

 

[Andrea Panza]

Hi Marcus,
For what I understand the information about space expansion is based on the redshift, but if we are falling in a giant black hole we could be able to observe only what is behind us in the fall (the bodies closer to the singularity are subject to a stronger gravitational field so the escape velocity that is already higher than the speed of light gets higher and higher and we don't see them). What passed the event horizon after we did is behind us and we are falling on the singularity with increasing speed so, although we are all falling on the same point, from our point of view it should look like that the space is expanding in an accelerated way (but in truth we are the one accelerating).
Probably this way of reasoning is wrong again, but I would like to hear your opinion about it.

Andrea

 

[marcus]

Hi Marcus,
For what I understand the information about space expansion is based on the redshift, but if we are falling in a giant black hole we could be able to observe only what is behind us in the fall (the bodies closer to the singularity are subject to a stronger gravitational field so the escape velocity that is already higher than the speed of light gets higher and higher and we don't see them). What passed the event horizon after we did is behind us and we are falling on the singularity with increasing speed so, although we are all falling on the same point, from our point of view it should look like that the space is expanding in an accelerated way (but in truth we are the one accelerating).
Probably this way of reasoning is wrong again, but I would like to hear your opinion about it.

Andrea

This sounds like a new question and a new topic of discussion. Feel free to start a new thread with a title that gives people an idea of what the new question is about. We seem to have concluded with this thread's question. I must excuse myself, supposed to go to a family birthday party in the city and I'm still trying to wake up. More coffee!

 

[Mordred]

Hi Marcus,
For what I understand the information about space expansion is based on the redshift, but if we are falling in a giant black hole we could be able to observe only what is behind us in the fall (the bodies closer to the singularity are subject to a stronger gravitational field so the escape velocity that is already higher than the speed of light gets higher and higher and we don't see them). What passed the event horizon after we did is behind us and we are falling on the singularity with increasing speed so, although we are all falling on the same point, from our point of view it should look like that the space is expanding in an accelerated way (but in truth we are the one accelerating).
Probably this way of reasoning is wrong again, but I would like to hear your opinion about it.

Andrea

If we were falling into a singularity with ever increasing speed. I doubt we would see an expansion. If you look at black hole models. They twist spacetime into swirls of a decreasing volume. As far as coming from a singurarity such as a BH. Well let's put it this way BH' s don't eat eveeything. Their feeding rates depend upon local materials. This results in inconsistent rates of materials. Within the BH this would generate a varying energy density. Our Universe is too homogeneous for that.

 

[Chronos]

Redshift of light from the universe entering the event horizon of a black hole is 2, not infinity. See http://www-e.uni-magdeburg.de/mertens/teaching/seminar/themen/touching_ghosts.pdf