[DBrow]

Hawking has a theory about small black holes, basically if the mass is less than Lunar, it will evaporate.

The hole evaporates by quantum tunneling (called in this case Hawking Radiation), and the rate is inversely proportional to mass so the smaller the mass, the higher the rate.

If LHC smacks two protons together and they make a black hole, the maximum mass is the relativistic mass of the two protons combined, which will be quite small.

The evaporation rate will be quite large, and the hole's lifetime very brief.

So if you integrate over the mass mu (hole mass to zero mass) and from time zero to time tau, you get

tau= C^2/(3K)mu^3

The evaporation time is proportional to the cube of the hole's mass.

K is the hole's Hawking temperature in K, and I neglect charge or spin.

The Hawking temperature is

T= (hbar C^3)/(8 pi G k m)

The larger the mass of the hole the lower the temperature. If the hole T is higher than the cosmic background, it will emit energy via quantum tunneling (this is the likely source of the 511 KeV radiation from Sag A*). The emission of Hawking radiation results in a mass decrease of the hole. Small hole, short lifetime.

I think a 100,000 kg hole would wink out in a second or less.

[who_would_fardels_bear]

So in order for there to be black holes at all, the black holes that exist had to have achieved critical mass rather quickly?

So I guess there is no way to aggregate a black hole. It has to be the result of some almost instantaneous phenomenon such as the rapid collapse of a star.