Hawking radiation: why black holes evaporate

1974: a black hole is not quite black

In the early 1970s, Jacob Bekenstein proposed that a black hole has an entropy proportional to the area of its horizon. Stephen Hawking was sceptical at first: an object with entropy should have a temperature, and therefore radiate, which a black hole cannot do. In 1974, by adding quantum mechanics to the calculation, he found that a black hole does radiate, exactly like a hot body.

Where does the radiation come from?

In quantum physics, the vacuum is not nothing: it is full of fluctuations. Near the horizon, spacetime is so curved that the vacuum seen by a distant observer no longer matches the local vacuum. The result: far from the black hole, you receive a flux of particles with a perfectly thermal spectrum. The energy carried away is taken from the black hole's mass, which shrinks.

A temperature set by the mass

The more massive the black hole, the colder it is. A Sun-mass black hole sits at about 6 × 10⁻⁸ kelvin, far colder than the Universe's relic radiation at 2.7 K: it absorbs more energy than it emits. Only black holes below roughly 60% of the Moon's mass would today be hotter than their surroundings.

Evaporation

As it loses mass, the black hole gets hotter, radiates more and loses mass even faster. Its lifetime grows as the cube of its mass: about 10⁶⁷ years for one solar mass. Primordial black holes of about 10¹¹ to 10¹² kg, if they exist, would be finishing their evaporation today; gamma-ray telescopes are searching for them, so far without success.

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Why it is a problem

Thermal radiation carries no trace of what fell into the black hole. If the black hole evaporates completely, where did the information go? Hawking asked the question in 1976; it has occupied theoretical physics ever since. This is the information paradox.