Is there a minimum mass for black holes?

[JK423]

Hi all,

I was (superficially) reading about the information loss paradox. Of what i understood it's based on the complete evaporation of the black hole via hawking radiation, so in some sense all the energy of a black hole will eventually become radiation.
The following question immediately popped up in my head, perhaps it's quite naive, i don't know. If a black hole is evaporated, that means that its mass will continuously decrease, right? The statement that the whole black hole will be evaporated, implies that it will evaporate radiation until its mass m→0. In turn, this implies that there exist black holes with m→0!

How is that possible? I see here a pretty obvious non-physical situation, that e.g. there exists black holes with masses of the order of nanograms (!) and less. How can an infinitesimally small mass create such a huge spacetime distortion? Somethings seems to be wrong here, isn't it?

Thanks for all the help beforehand :)

 

[stevendaryl]

Hi all,

I was (superficially) reading about the information loss paradox. Of what i understood it's based on the complete evaporation of the black hole via hawking radiation, so in some sense all the energy of a black hole will eventually become radiation.
The following question immediately popped up in my head, perhaps it's quite naive, i don't know. If a black hole is evaporated, that means that its mass will continuously decrease, right? The statement that the whole black hole will be evaporated, implies that it will evaporate radiation until its mass m→0. In turn, this implies that there exist black holes with m→0!

How is that possible? I see here a pretty obvious non-physical situation, that e.g. there exists black holes with masses of the order of nanograms (!) and less. How can an infinitesimally small mass create such a huge spacetime distortion? Somethings seems to be wrong here, isn't it?

Thanks for all the help beforehand :)

The distortion of spacetime by a black hole is not huge, except near the event horizon. So a tiny black hole will only make a big distortion when you are very close to the black hole.

 

[JK423]

The distortion of spacetime by a black hole is not huge, except near the event horizon. So a tiny black hole will only make a big distortion when you are very close to the black hole.

Thank you for our reply. So, as m→0 the radius of the horizon goes to zero as well. If there was an object inside the black hole of finite size (no matter how small), when the radious of the horizon got below the radius of the object then the black hole would cease to exist. Is that correct? The only option that this doesn't happen is for this object to have shrinked in a mathematical point, which is non-physical. It seems to me that the paradox is based on non-physical physics..

 

[Nugatory]

There is nothing in the equations of GR (google for "Schwarzschild metric" to get started) that requires a minimum size; they work just fine for arbitrarily small masses. And as for the physical plausibility of such thing, remember that the intense effects are concentrated in a very small area; at a distance of a few atomic radii, the gravitational effects of a nanogram-sized black hole are as negligible as those of any other nanogram mass.

There are, however, two reasons not to take this result at face value:
1) a nanogram-sized black hole would have a radius on the order of 10^-23 meters. It's not clear that we have any physical theory that works on that scale; certainly there's no reason to trust GR at these scales.
2) the only known process for creating black holes is gravitational collapse, which only works for black holes of stellar and larger mass. These have such low decay rates that none will have shrunk appreciably over the age of the universe. So even if these tiny black holes are theoretically possible, there's no reason to think that they actually exist.

 

[Bill_K]

Of what i understood it's based on the complete evaporation of the black hole via hawking radiation, so in some sense all the energy of a black hole will eventually become radiation.

To be clear, Hawking "radiation" consists of particles - of all kinds.

The statement that the whole black hole will be evaporated, implies that it will evaporate radiation until its mass m→0. In turn, this implies that there exist black holes with m→0!

As the mass gets smaller, the evaporation gets more rapid. Eventually a point is reached where the semiclassical argument that leads to Hawking radiation is no longer valid, and a full quantum treatment is required - which is currently beyond our reach. The smallest mass that a black hole can have classically is the Planck mass (for this term, see Wikipedia)

If there was an object inside the black hole of finite size (no matter how small), when the radious of the horizon got below the radius of the object then the black hole would cease to exist. Is that correct?

Anything that falls into a black hole does not remain a finite size. It is crushed by the singularity at r = 0.

 

[JK423]

Thanks a lot for the feedback!