Exploring Black Holes: Beyond the Hole

[Stavros Kiri]

Caution: I re-edited (a bit) my "Masswise" question after Labguy answered.

 

[Labguy]

That's based on the first option (pure evaporation - no explosion). I am looking for the critical mass right before burst (or explosion). Drakkith seems to have an idea.

From:
http://casa.colorado.edu/~ajsh/hawk.html in part reads:
"Evaporation of a mini black hole
Black holes get the energy to radiate Hawking radiation from their rest mass energy. So if a black hole is not accreting mass from outside, it will lose mass by Hawking radiation, and will eventually evaporate. For astronomical black holes, the evaporation time is prodigiously long - about 1061 times the age of the Universe for a 30 solar mass black hole. However, the evaporation time is shorter for smaller black holes (evaporation time t is proportional to M3), and black holes with masses less than about 1011 kg (the mass of a small mountain) can evaporate in less than the age of the Universe. The Hawking temperature of such mini black holes is high: a 1011 kg black hole has a temperature of about 1012 Kelvin, equivalent to the rest mass energy of a proton. The gravitational pull of such a mini black hole would be about 1 g at a distance of 1 meter.

It is not well established what an evaporating mini black hole would actually look like in realistic detail. The Hawking radiation itself would consist of fiercely energetic particles, antiparticles, and gamma rays. Such radiation is invisible to the human eye, so optically the evaporating black hole might look like a dud. However, it is also possible that the Hawking radiation, rather than emerging directly, might power a hadronic fireball that would degrade the radiation into particles and gamma rays of less extreme energy, possibly making the evaporating black hole visible to the eye. Whatever the case, you would not want to go near an evaporating mini black hole, which would be a source of lethal gamma rays and energetic particles, even if it didn't look like much visually."
I don't think an actual size can be calculated yet since we don't yet know anything about "singularity mass", The Hawking Radiation comes from the Event Horizon and not from the singularity. The BH temperature calculations are shown on the link but how do we connect a temperature with an EH size to get a size at evaporation, or explosion?

 

[Stavros Kiri]

From:
http://casa.colorado.edu/~ajsh/hawk.html in part reads:
"Evaporation of a mini black hole
Black holes get the energy ... or explosion?

Thanks! That helps. It seems there is no exact quantitative model yet for these sort of things, that would lead to a direct equation, yet.

 

[Drakkith]

That's based on the first option (pure evaporation - no explosion). I am looking for the critical mass right before burst (or explosion). Drakkith seems to have an idea.

I doubt there's a hard line between "explosion" and "right before the explosion" like there is in a bomb.

 

[Stavros Kiri]

I doubt there's a hard line between "explosion" and "right before the explosion" like there is in a bomb.

But if the mass is already zero before burst there would be no burst ... (and no black hole) , while there is indeed a bomb right before an explosion ...

When the size is critically small for burst, there must be a critical mass, but perhaps it's hard to calculate.

 

[Chronos]

The theoretical minimum for black hole mass is the Planck mass, which is about 22 micrograms. This has a mass energy equivalence of roughly 470 kilograms of TNT or about 1.22e+19 GeV.

 

[Stavros Kiri]

The theoretical minimum for black hole mass is the Planck mass, which is about 22 micrograms. This has a mass energy equivalence of roughly 470 kilograms of TNT or about 1.22e+19 GeV.

Now you are talking. I had forgotten that! ...

 

[Stavros Kiri]

Thus M_critical = Planck mass , and then ... Booom to zero!
At the same time the critical size runs down to the atomic scale.
So basically applying the uncertainty principle to calculate those, but correct me if I am wrong.

 

[Stavros Kiri]

Thus M_critical = Planck mass , and then ... Booom to zero!
At the same time the critical size runs down to the atomic scale.
So basically applying the uncertainty principle to calculate those, but correct me if I am wrong.

If that's the conclusion, it seems that PF cooperation brought some results here ...

 

[Stavros Kiri]

And one perhaps can go even further to interpret that "mysterious" dissapearence (complete evaporation) of the black hole as connected somehow to the uncertainty principle +/ the things we know about Hawking radiation ...

 

[Stavros Kiri]

ΔEΔt ~ h/2π to estimate the small lifetime of that atomic scale black hole [E calculated from Planck mass, etc.] ..., but perhaps there is more.

 

[Stavros Kiri]

Thus we get an idea how and why black holes die: once they get down to atomic scale (by Hawking radiation evaporation mechanism), they are bound to die fast, as dictated by the uncertainty principle ...
(+ thanks to Drakkith, Chronos, Labguy, Phinds, hsdrop, stoomart, Simon Peach etc.)

 

[phinds]

Thus we get an idea how and why black holes die: once they get down to atomic scale (by Hawking radiation evaporation mechanism), they are bound to die fast, as dictated by the uncertainty principle ...
(+ thanks to Drakkith, Chronos, Labguy, Phinds, hsdrop, stoomart, Simon Peach etc.)

Where did you get this? What does the HUP have to do with the final black hole evaporation/explosion/whatever ?

 

[Chronos]

The Compton wavelength might be more familiar

 

[Stavros Kiri]

Where did you get this? What does the HUP have to do with the final black hole evaporation/explosion/whatever ?

I explained it earlier:

https://www.physicsforums.com/threads/black-hole-question.897685/page-3#post-5649510

Prove your objection, if any. Open to suggestions etc.

 

[Stavros Kiri]

Where did you get this? What does the HUP have to do with the final black hole evaporation/explosion/whatever ?

In other words, you can't confine a black hole in atomic scale and with the relevant energy levels and have it live long at the same time! ... It will be unstable and will collapse within a matter of 0.1sec (as stootmart [based on Hawking (1974)] said earlier https://www.physicsforums.com/threads/black-hole-question.897685/page-2#post-5648676), and perhaps it's not just the Hawking radiation (evaporation) at this final stage of the BH (there may be another extra final mechanism [for the atomic scale] not clear yet ... (that brings the burst) [whose profound role, action, function and connection to the Uncertainty principle (HUP) could perhaps be explained with hidden variables, but I am not sure at this point] ).

 

[Stavros Kiri]

... within a matter of 0.1sec (as stootmart [based on Hawking (1974)] said earlier ...

My understanding according to Stephen Hawking's 1974 letter to Nature is it's both: the black hole evaporates and then explodes in the last 0.1 second.

That shows perhaps there must be two mechanisms ...

 

[Drakkith]

There is only one mechanism. Hawking merely says that in the final 0.1 seconds of its life a black hole would release about 1 million megatons of energy. He could have easily said how much energy was lost in the last 0.5 seconds or 1 nanosecond or some other amount of time.