We all know that a hole is a kind of cosmic funnel: it swallows everything that gets close enough to get caught in its gravitational field. The voracity of these remains of ancient stars can make our lives bitter. 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 graduate student of Jewish parents born in Mexico, proposed that the event horizon of a black hole (or point of no return, because if you go through it you are trapped forever inside) was a measure of its entropy Therefore, everything that was known about thermodynamics could be applied to black holes. In 1972, at the summer school in Les Houches in the French Alps, Hawking along with two great black hole experts, 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 to, but different from, the laws of thermodynamics” they claimed. But that year the great Russian theorist Yakov Zeldovich and his student Alexei Starobinsky showed that, by joining quantum mechanics with the equations of a rotating black hole, it turned out that it should emit some kind of radiation. Hawking didn’t believe it very much, 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 radiate and the laws he had formulated with Bardeen and Brandon were really the laws of black hole thermodynamics: “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 were not so strange 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 mathematical point, without dimensions, where all the mass of the star is concentrated, crushed by its own gravity. Considering such small sizes implies that possible quantum mechanical effects must be taken into account.
The first result of doing this is that black holes do not have zero entropy. In fact, they have much, 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 have it too, albeit extremely small: on the order of ten millionths of a degree above absolute zero for the smallest holes that can be seen. 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 have to emit energy. But, hadn’t we agreed that nothing can escape from its interior? Yes, Hawking replied. That energy comes right from its surface and not from within. Black holes are not black; They are gray.
Now, since the energy emitted is at the expense of that contained inside, then a black hole loses energy continuously. As in our bank accounts, the quantity we are interested in controlling is not the energy that goes out, but the net flow, profits minus losses. In black holes the calculation is simple. The universe is about 3 degrees above absolute zero, the temperature of the microwave background radiation, the oldest relic of the Big Bang. Since the smallest possible black hole (three solar masses) has a lower temperature than the microwave background, this means that the entire universe is hotter, so the black holes receive more energy than they emit.
But what if the temperature of the black hole were higher than that of the universe? It would then give off a large amount of energy by a mechanism known as Hawking evaporation . It is an accelerated process: by radiating energy by Hawking evaporation , the hole loses mass and having less mass, its temperature increases. This causes the difference in temperature with the outside to be greater, so it will radiate faster, lose more mass and increase its temperature even more rapidly. This accelerating spiral culminates in a tremendous explosion – and the disappearance of the hole – visible in the range of gamma radiation.
In a speculative display we could calculate the time that must pass for a classic black hole to completely disappear after throwing all its mass into space in the form of energy. With a small mass, about three solar masses, it will disappear after a whopping 1066 years. Knowing that the universe has existed for 1010 years, saying that the life of a black hole is 1056 times longer than the current universe is impossible to imagine. As much as saying that the radiated power is 10-24 watts: to emit as much light as a hundred watt light bulb we would need a hundred billion black holes.
References:
Hawking, S. W. (1975). Particle creation by black holes. Communications in Mathematical Physics, 43 (3): 199–220. doi:10.1007/BF02345020
Bardeen, J. M., Carter, B., Hawking, S. W. (1973). The Four Laws of Black Hole Mechanics. Communications in Mathematical Physics 31, pp. 161-170. doi:10.1007/BF01645742
Bekenstein, J.D. (1972) Black holes and the second law. Lett. Nuovo Cimento 4, 737–740. doi:10.1007/BF02757029
