Hawking radiation versus the cosmic background

[Swamp Thing]

Is the cosmic backround radiation incident on a black hole sufficient to make up for the energy lost through Hawking radiation?

And what if we include the average energy flux from discrete objects like galaxies, as seen in intergalactic space?

 

[Vanadium 50]

For BH's smaller than ~70 microns, Hawking radiation dominates and the BH will get smaller. For BH's larger than this, absorbing radiation dominates and the BH will get bigger.

 

[cosmik debris]

For BH's smaller than ~70 microns, Hawking radiation dominates and the BH will get smaller. For BH's larger than this, absorbing radiation dominates and the BH will get bigger.

Does this mean that the big black holes out there don't decay and go pop but just get bigger?

Cheers

 

[phinds]

Does this mean that the big black holes out there don't decay and go pop but just get bigger?

Cheers

Yes. For now. EVENTUALLY, Hawking radiation takes over and they get smaller and smaller. I've seen numbers like 10E80 years for total evaporation of big ones.

 

[Grinkle]

I've seen numbers like 10E80 years for total evaporation of big ones.

I am curious - by an Earth bound clock, or by the clock of an observer free-falling into the hole, or some different clock?

 

[phinds]

I am curious - by an Earth bound clock, or by the clock of an observer free-falling into the hole, or some different clock?

Earth-bound. Not that the Earth will be around for anything more than a totally trivial portion of that time. Better to call it a co-moving observer (and if you don't know exactly what that means, look it up)

 

[Vanadium 50]

Yes. For now. EVENTUALLY, Hawking radiation takes over and they get smaller and smaller

Is that true in general? Remember, Hawking radiation doesn't win until the BH is hotter than the CMBR, and while it is absorbing all that CMB radiation it is cooling.

 

[phinds]

Is that true in general? Remember, Hawking radiation doesn't win until the BH is hotter than the CMBR, and while it is absorbing all that CMB radiation it is cooling.

10E80 years is a LONG time, so yes.

 

[Vanadium 50]

10E80 years is a LONG time, so yes.

Yes, and it's absorbing radiation all this time, growing and cooling. Have you calculated that for a BH of any size it eventually evaporates? I suppose one could add for any time and any cosmology.

In short - can you show me a calculation or quantitative argument?

 

[phinds]

Yes, and it's absorbing radiation all this time, growing and cooling. Have you calculated that for a BH of any size it eventually evaporates? I suppose one could add for any time and any cosmology.

In short - can you show me a calculation or quantitative argument?

I don't have the calculation but I've seen that stat here several times. Eventually the CMB fades away, effectively, as does ALL radiation coming at a BH and Hawking Radiation takes over. Again, 10E80 is just a STAGGERINGLY long time.

 

[gneill]

The CMB is cooling as the universe expands. It started out at something like 3000K some 13.2 billion years ago and is now down to about 2.7K. Compared to 10^80 years, 13.2 billion is utterly insignificant.

 

[Vanadium 50]

gneil, you're right that the universe has a long time to cool. But by the same argument, the BH has a long time to accrete.

I'm not arguing 10^80 years is a short time. I am asking is there a mass so large that the CMBR accretion always exceeds Hawking radiation. Yes, both decrease with time, and yes, 10^80 years is a long time. My question is whether there exists a mass (and possibly a cosmology) where the two curves never cross. I am willing to believe there is, and I am willing to believe there isn't. But if possible, I'd like a more quantitative answer than "10^80 is big" or "I read somewhere".

 

[George Jones]

gneil, you're right that the universe has a long time to cool. But by the same argument, the BH has a long time to accrete.

I'm not arguing 10^80 years is a short time. I am asking is there a mass so large that the CMBR accretion always exceeds Hawking radiation. Yes, both decrease with time, and yes, 10^80 years is a long time. My question is whether there exists a mass (and possibly a cosmology) where the two curves never cross. I am willing to believe there is, and I am willing to believe there isn't. But if possible, I'd like a more quantitative answer than "10^80 is big" or "I read somewhere".

I knew that John Baez had written about this, so I looked it, and, interestingly, found

"But it would take a nontrivial calculation to show that reasonable-sized black holes have no chance of getting this big. I think it's true, but I haven't done the calculation.

For now, let's assume it's true: all black holes will eventually shrink away and disappear — none of them grow big enough to stick around when it gets really cold."

Baez's essay ca be found at
http://math.ucr.edu/home/baez/end.html

 

[Vanadium 50]

Thanks, George. Baez says that 10^32 solar masses is about the dividing line. There's no known process that produces BHs this size, but then again there's no known process that produces 70 um BHs either.