Questions about Hawking radiation and extremal black holes...?

[Suekdccia]

TL;DR

Are extremal black holes thermodynamically impossible for having a 0 Hawking temperature?

I'm studying if there is some way to avoid black hole evaporation, even if it requires a very special set up of conditions...

Theoretically, extremal black holes (both for rotating Kerr and Reissner-Nordström ones) would avoid evaporation as they would not emit Hawking radiation. Since perfectly extremal black holes would have a Hawking temperature of 0K, this presumably would violate the 3rd law of thermodynamics.

Then, are extremal black holes physically impossible?

Would nearly-extremal black holes avoid somehow evaporation? Or would they emit a small amount of Hawking radiation that would make them evaporate inevitably?

Can there be any way in which black holes avoid being evaporated? Or is it utterly inevitable?

 

[PeterDonis]

Can there be any way in which black holes avoid being evaporated? Or is it utterly inevitable?

Since we don't even have a full theory of black hole evaporation (all we have are approximate models that might or might not be correct), and since we have no evidence about it and aren't likely to get any any time soon, this question is not answerable. The best we can say is that this is still an open area of research.

 

[OlderWannabeNewton]

Are you specifically interested in black holes that don't evaporate, or black holes that don't emit any Hawking radiation? If it's the former then you can just put the black hole in AdS. If it's a large black hole (i.e. above the typical AdS length scale) then it won't evaporate because of the reflecting boundary conditions at infinity. The black hole will reach thermal equilibrium with the bath of Hawking radiation.

A non-extremal black hole will always emit Hawking radiation though, because of the non-zero temperature.

 

[Suekdccia]

A non-extremal black hole will always emit Hawking radiation though, because of the non-zero temperature.

I see. And would extremal black holes be impossible for their 0K temperature?

Also, would the AdS scenario that you described also work for dS spacetimes (which our universe is approaching into)?

 

[Demystifier]

Both classical and semiclassical gravity predict that they are impossible by the 3rd law of black hole thermodynamics.