Hawking radiation predicts that black holes can slowly evaporate through the eff

Question

Hawking radiation predicts that black holes can slowly evaporate through the effective emission of a particle. This particle is a real particle, as in, it is not a black hole itself. I'll write this (a bit tongue-in-cheek) as follows, with A being the emitted particle, and black hole prime being the black hole with slightly reduced mass.

There is every reason to think this continues until the black hole stops being a black hole. So we are left with a radiated particle and something else. We don't know much about this process, but I think we can still limit it to a 2-product decay.

What could the something else, B, be? I don't know much about it, but I know that it is:

Not a black hole
A physically plausible particle

It might be more realistic to ask what other conditions should we impose on B? I realize this is probably an unsolved problem. Also, won't A be really highly energetic? How energetic? Actually, what is A to begin with?

Hawking radiation predicts that black holes can slowly evaporate through the effective emission of a particle. This particle is a real particle, as in, it is not a black hole itself. I'll write this (a bit tongue-in-cheek) as follows, with A being the emitted particle, and black hole prime being the black hole with slightly reduced mass. block hole -- > A + B What could the something else, B, be? I don't know much about it, but I know that it is: Not a black hole A physically plausible particle It might be more realistic to ask what other conditions should we impose on B? I realize this is probably an unsolved problem. Also, won't A be really highly energetic? How energetic? Actually, what is A to begin with? black hole -- > A + black hole There is every reason to think this continues until the black hole stops being a black hole. So we are left with a radiated particle and something else. We don't know much about this process, but I think we can still limit it to a 2-product decay.

Explanation / Answer

Most of the time while the black hole is evaporating, the "A" particles will be photons (or other mass-less particles like gravitons). The reason for this is that the black hole emits radiation as if it were a black body and the temperature of the black body is inversely proportional to the black hole mass. For black holes with mass equal to the mass of the sun the temperature would be 60 nano-kelvins. So the energy of the particles emitted would have to be extremely low which is why they need to be mass-less particles like photons or gravitons.

Now in our universe (today), if the mass of the black hole is greater than about the mass of the moon, it would actually gain more energy from the cosmic microwave background radiation than it would lose to Hawking radiation since the black body temperature of black hole with a mass greater than the moon would be lower than the CMB black body temperature of 2.7 K. The CMB temperature decreases over time so eventually all black holes will evaporate but it will take an extremely long time for this to happen.

However as the black hole gets smaller and smaller, the black body temperature rises so that eventually the temperature would rise so high that massive particles could be emitted. For a given amount of energy being emitted any particle that has a rest mass below that energy could be the emitted particle. The reason for this is that the Hawking radiation is a result of the vacuum virtual pair creation in the vicinity of the event horizon. Since all particles participate in the vacuum virtual pair creation, any particle that is compatible with that black body energy spectrum will be emitted.

When the mass of the black hole approaches zero, the black body temperature will approach infinity so the evaporation will be faster and faster with more and more energetic particles. So the last two particles that would be emitted would be any 2 particles compatible with the remaining mass of the micro-black hole.

So if, for example, a micro-black hole could be created at the LHC it would evaporate very rapidly into an isotropic spray of particles of all types compatible with the energy of the black hole. That would be the event signature that would be found by the LHC detectors.

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