Mass In vs. Mass Out

Okay, so black holes radiate out into space and lose mass. It's just that simple, right? Not really. Cosmic background radiation is constantly feeding the black hole lots of energy, steadily giving the black hole more mass. Eventually, though, the universe will cool enough such that the black hole radiates faster than the background radiation can replenish the lost mass. How long does it take to reach equilibrium between the opposing powers? A LONG time. Here's the scoop:

Through the quantum process known as Hawking radiation, black holes can actually lose mass by evaporating one member of a particle-antiparticle pair. The black hole radiates as a blackbody with a temperature inversely proportional to mass. Since black holes are extremely massive objects, they radiate at very low temperatures. For example, a solar mass black hole has a temperature of about 6*10^-8 K. By radiating particles, the black hole slowly loses mass until it completely dries up and disappears in a burst of energy.

A black hole, however, absorbs all incident radiation. The cosmic background radiation left from the Big Bang constantly feeds a black hole with energy. Since a black hole is continually absorbing the cosmic background radiation, it is constantly gaining mass. Consequently, a large enough black hole in a hot enough universe experiences a net gain in mass. High cosmic background radiation temperatures can easily feed a large black hole enough mass to overcome the virtually insignificant Hawking radiation.

Does this mean that black holes will forever gain mass, never radiating quickly enough to eventually disappear? No. The expanding universe cools at a rate inversely proportional to the age of the universe. Currently, the cosmic background radiation temperature is about 2.7 K. This temperature is definitely hot enough to dominate the net change in mass of a solar mass black hole. After enough time has passed, however, the universe will become too cold to replace the mass lost to Hawking radiation. At this point, the black hole will begin to experience a net mass loss. The equilibrium point at which rate mass loss through Hawking radiation equals rate mass gain through background radiation absorption can be determined. Check it out!

For a solar mass black hole, the time to reach equilibrium is about 4.41*10^36 seconds, or 1.40*10^29 years. Estimating the current age of the universe to be 20 billion years, the time to reach equilibrium for a solar mass black hole is 7.00*10^18 times as long as the universe is currently old. Don't hold your breath!