Black holes are sites of immense gravitational attraction into which surrounding matter is drawn by gravitational forces. It was originally thought that the gravitation was so powerful that nothing, not even radiation, could escape from the black hole, but Hawking theorized that (particle-antiparticle) radiation would be emitted from just beyond the event horizon. This radiation does not come directly from the black hole itself, but rather is a result of virtual particles being "boosted" by the black hole's gravitation into becoming real particles. This would sap some of the black hole's energy, and so when these particles escape the black hole would lose a small amount of mass.
A black hole of one solar mass has a temperature of only 60 nanokelvin; in fact, such a black hole would absorb far more cosmic microwave background radiation than it emits. A black hole of 4.5 × 10²² kg (about the mass of the Moon) would be in equilibrium at 2.7 kelvin, absorbing as much radiation as it emits. Yet smaller primordial black holes would emit more than they absorb, and thereby lose mass.
The power emitted by a black hole in the form of Hawking radiation can easily be estimated for the simplest case of a nonrotating, non-charged Schwarzschild black hole of mass M. Wikipedia contains all the necessary ingredients: the formula for the Schwarzschild radius of the black hole, the Stefan-Boltzmann law of black-body radiation, the above formula for the temperature of the radiation, and the formula for the surface area of a sphere (the black hole's event horizon). Combining all these formulae, the emitted power comes out as:
The power in the Hawking radiation from a solar mass black hole turns out to be a minuscule 10−28 watts. It is indeed an extremely good approximation to call such an object 'black'.
Under the assumption of an otherwise empty universe, so that no matter or cosmic microwave background radiation falls into the black hole, it is possible to calculate how long it will take for the black hole to evaporate. The black hole's mass is now a function M(t) of time t. Taking the time derivative of Einstein's famous equationE = Mc², we get
leading to
which, assuming then mass is M0 at time t = 0, has the solution
Finally, setting M(tev) = 0 we get the time it takes the black hole to evaporate:
For a black hole of one solar mass, we get an evaporation time of 1067 years—much longer than the current age of the universe. But for a black hole of 1011 kg, the evaporation time is about 3 billion years. This is why some astronomers are searching for signs of exploding primordial black holes.
