The Black Hole Explosions

The lower the mass of the black hole, the higher its temperature is. So as the black hole loses mass, its temperature and rate of emission increase. It therefore loses mass more quickly. What happens when the mass of the black hole eventually becomes extremely small is not quite clear. The most reasonable guess is that it would disappear completely in a tremendous final burst of emission, equivalent to the explosion of millions of Thermonuclear bombs.

A black hole with a mass a few times that of the sun would have a temperature of only one ten-millionth of a degree above absolute zero. This is much less than the temperature of the microwave radiation that fills the universe, about 2.7 degrees above absolute zero — so such black holes would give off less than they absorb, though even that would be very little. If the universe is destined to go on expanding forever, the temperature of the microwave radiation will eventually decrease to less than that of such a black hole. 

 The black hole will then absorb less than it emits and will begin to lose mass. But, even then its temperature is so low that it would take about 10⁶⁶ years to evaporate completely. This is much longer than the age of the universe, which is only about 10¹⁰ years.

There might be primordial black holes with a very much smaller mass that were made by the collapse of irregularities in the very early stages of the universe. Such black holes would have a much higher temperature and would be emitting radiation at a much greater rate. A primordial black hole with an initial mass of a thousand million ton would have a lifetime roughly equal to the age the universe. Primordial black holes with initial masses less than this figure would already have completely evaporated. However, those with slightly greater masses would still be emitting radiation in the form of X rays and gamma rays. These are like waves of light, but with a much shorter wavelength. Such black holes hardly deserve the epithet black. They really are white hot, and are emitting energy at the rate of about ten thousand megawatts.

 

One such black hole could run ten large power stations, if only we could harness its output. This would be rather difficult, however. 

The black hole would have the mass of a mountain compressed into the size of the nucleus of an atom. If you had one of these black holes on the surface of the Earth, there would be no way to stop it falling through the floor to the center of the Earth. It would oscillate through the Earth and back, until eventually it settled down at the center. So the only place to put such a black hole, in which one might use the energy that it emitted, would be in orbit the Earth would be to attract it there by towing a large mass in front of it, rather like a grass in front of a horse. This does not sound like a very practical proposition, at least not in the immediate future...

We can calculate the temperature of black hole, By using this equation: