Ask Ethan # 57: How do black holes die?

The most dense and massive objects of the universe live terribly long, but not forever. And so what happens to them

Before the fact, sit like a child, and get ready to part with any prejudice, following modestly where and to what would the abysses of nature lead to, or you will not learn anything.
- T. G. Huxley

Imagining black holes, you are probably thinking of superdense and very massive parts of space, from which nothing can escape. Neither matter, nor antimatter, nor even light! You may also think that they continue to eat everything that was not fortunate enough to encounter them, even dark matter. But at some point, any black hole in the universe will not only end up growing, but also begin to decrease, lose mass, until it completely evaporates! This week in our column we will answer the question of Pavel Zhozhelsky, who asks:

I often saw an explanation of Hawking's radiation like: “pairs of virtual particles appear on the event horizon. One falls into the hole, the other runs away, taking with it a piece of the mass of the hole. ” And usually in small print it is indicated that this is a simplification. Perhaps this is the case - because if one of the particles falls into a hole, its mass should increase by the mass of the particle. What's the catch?

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This is a very complex topic, but one that we understand. Let's start with a discussion of how empty space looks.



In the general theory of relativity, space and time have an intricate connection, and form a four-dimensional fabric of space-time. If you remove all particles in the Universe for an infinitely long distance from the point you need, if you remove the fact of space expansion from the equations, if you also eliminate all types of radiation, and the curvature of space, you can say that you have created a flat empty space.

But when you start to take into account that you live in the Universe, where all particles and their interactions are governed by quantum field theory, you will have to admit that even in the absence of physical particles, the physical fields that control their interactions will not go away. One of the consequences of this will be that the entity we conceive of as “flat empty space” is not free from energy. Instead, one should imagine flat empty space as a quantum vacuum, where there are quantum fields everywhere.



You may be familiar with the idea that there are inherent in the space uncertainties of specific parameters on quantum scales in the Universe. We cannot simultaneously know the location and momentum of a particle, and the better we measure one of them, the greater the uncertainty of the second. The same relationship of uncertainties is characteristic of energy and time, which is important for us now.

If you observe what you imagine as empty space, but at the same time observe it at a certain point in time, you need to take into account that a moment is an infinitely small period of time. Because of this relationship of uncertainties, there is a huge uncertainty in the total amount of energy contained even in empty space at this time. This means that there may, in principle, be several pairs of particles and antiparticles that exist for very short periods of time, as long as they obey the well-known conservation laws in force in the physical Universe.



We often hear an explanation like “particle-antiparticle pairs appear and disappear in a quantum vacuum”, and although this explanation is quite obvious, this is not exactly what is happening. There are no real particles in the sense that if you launch a photon or an electron through this region of space, they will never be reflected from a particle of quantum vacuum. This description gives us the opportunity to look into the "quivering" inherent in the quantum vacuum, and shows that there is a reservoir of virtual particles, allowing us to treat the energy inherent in the empty space as the sum of all these virtual particles.

I repeat, because this is important: there is energy inherent in the empty space itself, and it can be represented as the sum of the quantum fluctuations inherent in this space.



Let's go further. Imagine that space, instead of being flat and empty, is still empty, but already curved - that is, deviations exist in the gravitational field of space.



What will our quantum fluctuations look like? In particular, if we allow space to bend due to the presence of a black hole, how will they look outside and inside the event horizon?

The questions are good, and most often in search of an answer you will see the following (incorrect) picture, which is the essence of Paul’s question:



If one imagines particle / antiparticle pairs as real ones, and if one escapes from the black hole, and the other falls beyond the event horizon, it turns out that energy has increased in the Universe: half outside the black hole and half to the black hole mass. But these pairs of particles and antiparticles are not real, but represent only a way of visualizing and counting the energy inherent in space.

The fact is that with a curved space, as you remember, there are deviations of the gravitational field. We use fluctuations to help visualize the energy inherent in empty space, but fluctuations can occur that begin outside the event horizon, which will fall inside the horizon without re-annihilation. But you can't steal energy from empty space - something must happen to save it. Therefore, each time a virtual particle (or antiparticle) falls inside, a real photon (or a set of them) should appear to compensate. And this real photon, leaving the event horizon, and carries energy from the black hole.



The way we used to visualize the process, when one of a pair of particles fell and the other escaped, is too naive to be useful, since it is not particles or antiparticles that contribute to the reduction of black holes, but photons corresponding to the black body spectrum.

I prefer the picture better, although it is still pretty naive. Imagine quantum fluctuations, in which each time you have a particle-antiparticle pair, one of which falls inside, another particle-antiparticle appears, in which the other falls. The remaining vapor from the particle and antiparticle annihilates, emitting real photons, and those that fall inward take the corresponding amount of mass (E = ms ² ) from the black hole.



This is still not a perfect analogy (because it is just an analogy), but at least photons leave the event horizon, which is consistent with Hawking radiation predictions. In fact - although you will have to make calculations of quantum field theory in a curved space-time to find out - Hawking radiation predicts that the photon spectrum will correspond to an absolutely black body with a temperature given:


which gives a temperature less than one micro Kelvin for a black hole with a mass equal to the mass of the Sun, less than one pico Kelvin for a black hole in the center of our galaxy, and only a few tenths of attoKelvin for the largest known black hole. The reduction rate to which this radiation corresponds is so small that black holes will grow, even if they absorb one proton over a period of time comparable to the age of our Universe — this will continue for about 10 to ²⁰ years.

After that, black holes with mass from the Sun will finally lose due to Hawking radiation, on average, more energy than they absorb, and completely evaporate in 10 ⁶⁷ years, and the largest of them - in 10 ¹⁰⁰ years. This may greatly exceed the age of the universe, but it is not forever. And they will decrease due to Hawking radiation, emitting photons.



As a result: empty space has zero-level energy, which is not zero, and in a curved space on the horizon of a black hole's events a low-energy emission spectrum of an absolutely black body appears. This radiation takes away the mass from the black hole and slightly compresses the event horizon with time. If you insist on representing the source of this radiation as particle / antiparticle pairs, at least represent two pairs at a time. Then the particle from one pair and the antiparticle from the other annihilate, creating real photons leaving the black hole, and the other virtual pair of particles falls into the hole and takes its energy (or mass).

That's how black holes and die! Thank you for the great question, Pavel, and if you have questions or suggestions, send them to me.