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When humans starve, they grow thin and eventually die; when a black hole starves, it too grows thin and dies … but it does so very spectacularly, in a burst of Hawking radiation.
At least that’s the way we understand it today (no black-hole-pining-away has yet been observed), and the theory may be wrong too.
Cosmologist, astrophysicist, and physicist Stephen Hawking showed, in 1974, that black holes should emit electromagnetic radiation with a black body spectrum; this process is also called black hole evaporation. In brief, this theoretical process works like this: particle-antiparticle pairs are constantly being produced and rapidly disappear (through annihilation); these pairs are virtual pairs, and their existence (if something virtual can be said to exist!) is a certain consequence of the Uncertainty Principle. Normally, we don’t ever see either the particle or antiparticle of these pairs, and only know of their existence through effects like the Casimir effect. However, if one such virtual pair pops into existence near the event horizon of a black hole, one may cross it while the other escapes; and the black hole thus loses mass. A long way away from the event horizon, this looks just like black body radiation.
It turns out that the smaller the mass a black hole has, the faster it will lose mass due to Hawking radiation; right at the end, the black hole disappears in an intense burst of gamma radiation (because the black hole’s temperature rises as it gets smaller). We won’t see any of the black holes in the Milky Way explode any time soon though … not only are they likely still gaining mass (from the cosmic microwave background, at least), but a one sol black hole would take over 10^67 years to evaporate (the universe is only 13 billion years old)!
There are many puzzles concerning black holes and Hawking radiation; for example, black hole evaporation via Hawking radiation seems to mean information is lost forever. The root cause of these puzzles is that quantum mechanics and General Relativity – the two most successful theories in physics, period – are incompatible, and we have no experiments or observations to help us work out how to resolve this incompatibility.
Some Universe Today stories which include Hawking radiation are Synthetic Black Hole Event Horizon Created in UK Laboratory, How to Escape from a Black Hole, and When Black Holes Explode: Measuring the Emission from the Fifth Dimension.
Black Holes Big and Small, and The Large Hadron Collider and the Search for the Higgs-Boson are two Astronomy Casts relevant to Hawking radiation.