Stephen HawkingBlack Holes? Been There, Bent That.

The sticker says Black Holes? Been There, Bent That. Hawking never said it; the line is ours. What he did say, in 1974, was stranger: black holes are not completely black.

In 1973 Jacob Bekenstein proposed that a black hole has entropy proportional to the area of its horizon. Hawking at first doubted it, because anything with entropy and energy has a temperature, and anything with a temperature glows. Then he did the calculation, applying quantum field theory to the curved spacetime outside a horizon, and found that it does glow. The first formula on this page is the temperature he obtained. Mass sits in the denominator: the bigger the black hole, the colder it is.

For a black hole with the mass of the Sun, that temperature is about 62 billionths of a kelvin. The cosmic microwave background around it is about 2.7 kelvin, tens of millions of times warmer, so such a black hole absorbs more radiation than it emits and is growing, not shrinking. Only a very small black hole, if any exist, would be hot enough to evaporate on a timescale that matters. Hawking radiation has never been detected from a real black hole.

The second formula is the entropy, with the factor of one quarter that Hawking's temperature fixed. For a solar-mass black hole it comes to about 10⁷⁷ times Boltzmann's constant. Entropy counts hidden arrangements. Of what?

That leads to the open question. If a black hole evaporates completely into thermal radiation, what becomes of the information about whatever fell in? In 1976 Hawking argued that it is destroyed, which ordinary quantum mechanics does not allow. Many physicists now expect it is preserved somehow. How is unsettled: the black hole information paradox is still open.

The sticker bends. The black hole, eventually, leaks.