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Quantum mechanical Thoughts on Black Holes

Annnaxim
Posts: 243
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9/29/2016 6:34:29 PM
Posted: 2 months ago
What is at the centre of a black hole? Is it a singularity as Einstein's theory suggests, or is it a quantum mechanical nutshell?

Black Holes radiate energy called Hawking-Radiation. But... what IS Hawking Radiation?
In 1973 Stephen Hawking also postulated, that every black hole has a temperature proportional to its gravity at its event horizon. Small black holes have a higher temperature than larger ones, which could be the reason why small black holes radiate at a greater rate.

Does this radiation consist of particles that appear out of nothing? Or is it a thermodynamic result of the Hawking-Temperature of the black hole?

So... WHAT IS A Black Hole?
Is a black hole a radiator of particles, or is it just a kind of Planck radiator of energy?
keithprosser
Posts: 2,084
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9/30/2016 6:48:13 AM
Posted: 2 months ago
As I understand it, Hawking radiation is due to gravity at the edge (or event horizon) of the BH splitting the matter/anti-matter pairs that appear everywhere due to quantum fluctutions. At the event horizon the anti-matter particle falls into the BH and the matter particle flies off. The infalling anti-particle reduces the mass of the BH, eventually causing the BH to disappear. The particle that flies off is what constitures 'Hawking radiation'.

Hawking caclulated that the spectrum (ie spread of energies) of the particles escaping from the BH of a given area was identical to the spectrum of thermal raditation emited by regular objects at a particular temperature so in that sense one could speak of the temperature of the surface of a BH.

Larger BHs have lower temperatures, but as described above BHs get smaller due to infalling anti-particles. As they get smaller, they get hotter and the Hawking radiation increases, resulting in the shrinkage accelerating. This is a 'positive feeback' effect and results in BHs eventually emitting a huge burst of Hawking radiation as it finally disappears.

I will not be offended if anyone chooses to point out the flaws and over-simplifications in the above...!
dee-em
Posts: 6,490
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9/30/2016 12:46:12 PM
Posted: 2 months ago
At 9/30/2016 6:48:13 AM, keithprosser wrote:
As I understand it, Hawking radiation is due to gravity at the edge (or event horizon) of the BH splitting the matter/anti-matter pairs that appear everywhere due to quantum fluctutions. At the event horizon the anti-matter particle falls into the BH and the matter particle flies off. The infalling anti-particle reduces the mass of the BH, eventually causing the BH to disappear. The particle that flies off is what constitures 'Hawking radiation'.

I'm not sure that anything dictates which particle (matter or anti-matter) is emitted from the BH. I would have thought it was random. Can you explain?

Hawking caclulated that the spectrum (ie spread of energies) of the particles escaping from the BH of a given area was identical to the spectrum of thermal raditation emited by regular objects at a particular temperature so in that sense one could speak of the temperature of the surface of a BH.

Larger BHs have lower temperatures, but as described above BHs get smaller due to infalling anti-particles. As they get smaller, they get hotter and the Hawking radiation increases, resulting in the shrinkage accelerating. This is a 'positive feeback' effect and results in BHs eventually emitting a huge burst of Hawking radiation as it finally disappears.

I will not be offended if anyone chooses to point out the flaws and over-simplifications in the above...!
dee-em
Posts: 6,490
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9/30/2016 12:50:40 PM
Posted: 2 months ago
At 9/29/2016 6:34:29 PM, Annnaxim wrote:
What is at the centre of a black hole? Is it a singularity as Einstein's theory suggests, or is it a quantum mechanical nutshell?

There is a hyothesis that there is no centre or singularity. Matter certainly spirals towards the centre but because of extreme time dilation due to the enormous gravity it never gets there before the black hole eventually evaporates during the heat death phase of the universe.

Black Holes radiate energy called Hawking-Radiation. But... what IS Hawking Radiation?
In 1973 Stephen Hawking also postulated, that every black hole has a temperature proportional to its gravity at its event horizon. Small black holes have a higher temperature than larger ones, which could be the reason why small black holes radiate at a greater rate.

Does this radiation consist of particles that appear out of nothing? Or is it a thermodynamic result of the Hawking-Temperature of the black hole?

So... WHAT IS A Black Hole?
Is a black hole a radiator of particles, or is it just a kind of Planck radiator of energy?
keithprosser
Posts: 2,084
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9/30/2016 4:02:53 PM
Posted: 2 months ago
Hi DM.

I said I would accept being corrected! I did mis-remember something and it is indeed not the anti-particle is the one that always falls in. Rather whichever one falls in has, or acquires, 'negative energy' and the one that escapes has 'positive energy' (because the net energy must be zero). It is the negative energy of the in-falling particle (or anti-particle) that gives it 'negative mass' (by e=mc2) which when absorbed by the BH results in the BH losing mass.

I think the rest of what I wrote is not too far off, in a hand-wavy very approximate and informal way. The real physics and equations are above my pay-grade!

Speculatively, I'd guess what resides at the centre of a BH is not a literal singularity (because a literal singularity has various 'infinite' quantities), but something as close to 'a geometric point of infinite density' as allowed by quantum physics. But as a theory of 'quantum gravity' is still to be found I await further developments - which I hope I will remember somewhat better!
Annnaxim
Posts: 243
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9/30/2016 7:10:07 PM
Posted: 2 months ago
At 9/30/2016 6:48:13 AM, keithprosser wrote:

I will not be offended if anyone chooses to point out the flaws and over-simplifications in the above...!

This excellent article explains why virtual particles don't really exist.
Misconceptions about virtual particles: https://www.physicsforums.com...
Even though it may be technically correct, I find this to be rather purist view by mathematician.

As long as great Physicists like Steven Weinberg, Leonard Susskind, Richard Feynman, Lawrence Krauss, Brian Greene or Sean Carroll use them, I see no reason to give up the concept of virtual particles as the explanation for what happens in a quantum vacuum, at the event horizon of black holes, or what has been experimentally proven in the Casimir experiments or with the Lamb shift.
dee-em
Posts: 6,490
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9/30/2016 10:58:40 PM
Posted: 2 months ago
At 9/30/2016 4:02:53 PM, keithprosser wrote:
Hi DM.

I said I would accept being corrected! I did mis-remember something and it is indeed not the anti-particle is the one that always falls in. Rather whichever one falls in has, or acquires, 'negative energy' and the one that escapes has 'positive energy' (because the net energy must be zero). It is the negative energy of the in-falling particle (or anti-particle) that gives it 'negative mass' (by e=mc2) which when absorbed by the BH results in the BH losing mass.

Good. It kind of opens up the possibility of harvesting black holes for anti-matter as a fuel source for our distant descendants. Yeah, we can dream. :-)

I think the rest of what I wrote is not too far off, in a hand-wavy very approximate and informal way. The real physics and equations are above my pay-grade!

Me too. I'm strictly a fascinated amateur.

Speculatively, I'd guess what resides at the centre of a BH is not a literal singularity (because a literal singularity has various 'infinite' quantities), but something as close to 'a geometric point of infinite density' as allowed by quantum physics. But as a theory of 'quantum gravity' is still to be found I await further developments - which I hope I will remember somewhat better!

Yes, my intuition is that the universe does not permit infinities which would rule out a singularity.
Dirty.Harry
Posts: 1,589
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10/1/2016 4:26:01 PM
Posted: 2 months ago
At 9/29/2016 6:34:29 PM, Annnaxim wrote:
What is at the centre of a black hole? Is it a singularity as Einstein's theory suggests, or is it a quantum mechanical nutshell?

Black Holes radiate energy called Hawking-Radiation. But... what IS Hawking Radiation?
In 1973 Stephen Hawking also postulated, that every black hole has a temperature proportional to its gravity at its event horizon. Small black holes have a higher temperature than larger ones, which could be the reason why small black holes radiate at a greater rate.

Does this radiation consist of particles that appear out of nothing? Or is it a thermodynamic result of the Hawking-Temperature of the black hole?

So... WHAT IS A Black Hole?
Is a black hole a radiator of particles, or is it just a kind of Planck radiator of energy?

Black holes have been hypothesized since the late 18th century, Laplace discussed them, stars whose gravitation was so strong light could not be seen from them. His work (if I recall) was simply based upon the escape velocity, what size/mass etc would a star need for the escape velocity to exceed the speed of light.

That's it.