Q&A: Black Holes

Q:
I would like to know how black holes evaporate. What is meant by "Hawking Radiation"? Who proposed this theory that black holes evaporate and how? Also, after evaporating, where do black holes go or what do they form?

A:
Stephen Hawking wrote a paper in 1976 called "Black Holes and Thermodynamics" in which he states that thermodynamics, the study of bodies with temperatures greater than absolute zero, applies also to black holes.

He shows that black holes can be considered to have entropy, and since entropy is a measure of the heat divided by the temperature, we can find the temperature of the black hole if we also know its heat (which we do because the heat is directly related to the mass, or, more correctly, the mass-energy of the black hole).

After he shows that black holes have a non-zero temperature, by the laws of thermodynamics it will radiate energy and evaporate. Evaporation is not an easy process to understand, it takes quantum electrodynamics to calculate the rate of evaporation and to give a physical process by which it takes place. Maybe you've heard of the Heisenberg uncertainty principle, which states that the energy of an object will always be uncertain by a very very small amount divided by the time over which you measure the energy of the object. That's not easy to understand unless you've taken some physics classes, but it seems from your question that you have. By this principle you may produce a pair of particles in space, creating energy and breaking the law of conservation of energy, IF you do so in a very short amount of time. So you can have a pair of particles pop out of nothing, as long as they disappear almost instantaneously, and in this case they are called virtual particles. In order to conserve other quantities, one particle is the anti-particle of the other, so that you might see an electron-positron pair. Somehow, near the intense curvature of the black hole, the pair may become real in a process I don't understand myself, somehow the strong gravitational field is able to impart energy to the pair and make it real. But one particle may fall into the black hole and the other may escape. The particle that escapes the event horizon (the edge or point of no return of the black hole) goes out into space. It turns out that if you calculate the rate of virtual pair production near the event horizon of a black hole, you get the same rate predicted by thermodynamics for the cooling off of a body that has the temperature of the black hole. So, one can think of the particles that escape the black hole after being pair produced as being the evaporated particles of the black hole.

This process takes a long long time. Even for a small black hole, the size of the Sun, it would take many more times than the age of the universe for it to evaporate. And after it evaporates, there should be a naked singularity, a point of infinite density without an event horizon. But really, no one knows what is left after it evaporates.

There are 2 interesting papers on the web, both of them published science papers so will be tough to read although the introductions are usually accessible. The first is from a scientist dubious about the existence of Hawking radiation:
http://xxx.lanl.gov/abs/gr-qc/0304042
and the second attempts to understand how quantum mechanics applies to black holes:
http://xxx.lanl.gov/abs/gr-qc/9803049

More basic questions and answers that I think you will find interesting may be found in our black hole question and answer pages:
http://chandra.harvard.edu/resources/faq/black_hole/bhole-main.html