Do black holes evaporate?

We all know that a hole is a kind of cosmic funnel: it swallows everything that comes close enough to be trapped in its gravitational field. The voracity of these remains of ancient stars can make our lives miserable. By swallowing everything, be it light or atoms, it increases its energy, or what is the same, its mass. Now, there is a well-known result of thermodynamics that says that all bodies, even the coldest – unless they are at absolute zero – emit, and therefore lose, energy. But by definition, nothing escapes from a black hole, so they can’t radiate anything. The conclusion is obvious: if they do not emit, they must be at absolute zero temperature (-273 degrees Celsius). Furthermore, and according to thermodynamics, a body at absolute zero has zero entropy (a concept related to the amount of disorder in a system). Final point.

In 1971, Bekenstein, a Mexican-born graduate student of Jewish parents, proposed that the event horizon of a black hole (or point of no return, because if you go through it you’ll be trapped inside forever) was a measure of its entropy. Therefore, everything that was known about thermodynamics could be applied to black holes. In 1972, at the Les Houches summer school in the French Alps, Hawking together with two leading experts on black holes, James Bardeen and Brandon Carter, derived four laws of black hole mechanics that closely resembled those of thermodynamics, but they refused to accept that they really were: “they are similar, but different, to the laws of thermodynamics” they affirmed. But that year the great Russian theorist Yakov Zeldovich and his student Alexei Starobinsky showed that, by combining quantum mechanics with the equations of a rotating black hole, it followed that it should emit some kind of radiation. Hawking didn’t quite buy it, but enough to be intrigued by the possibility. So he began to study it.

In 1974 his calculations revealed that Bekenstein was right: black holes radiated and the laws he had formulated with Bardeen and Brandon were actually the laws of thermodynamics for a black hole: “I was really sad because it destroyed my whole theoretical framework, and I did what I could to get rid of this result. I was quite irritated,” he would confess years later.

Playing with quantum mechanics and general relativity, Hawking determined that black holes weren’t so weird after all. The problem was in the very conception of the black hole. The general theory of relativity is a classical theory, which does not take quantum effects into account. And yet, the absolute protagonist of a black hole is the central singularity, a dimensionless mathematical point where all the mass of the star, crushed by its own gravity, is concentrated. Considering such small sizes implies that possible quantum mechanical effects must be taken into account.

The first result of doing so is that black holes do not have zero entropy. In fact, they have much more than the stars from which they come. The second shows that black holes are not at absolute zero temperature. Any body with mass -energy- and entropy must be at a temperature other than zero and black holes also have it, even if it is extremely small: on the order of ten millionths of a degree above absolute zero for the smallest holes that can be form by stellar evolution. In fact, there is a basic rule: the more mass a black hole has, the lower its temperature. The third result is a consequence of the previous one. If it is not at zero temperature, it will need to emit energy. But, hadn’t we agreed that nothing can escape from inside? Yes, Hawking replied. That energy comes right from its surface and not from within. Black holes are not black; They are gray.