A group of physicists from three countries proposed a solution to the paradox of the disappearance of information in a black hole with “quantum hair”: matter inside a black hole at the quantum level encodes information in the external gravitational field, which in turn affects Hawking radiation. In the first paper published in the journal Physical Review Letters, physicists have proved the dependence of the states of gravitons outside the black hole on the state and distribution of matter inside it. In the second work published in the journal Physics Letters Bscientists have explained how this connection carries out the unitary evaporation of a black hole.
In his 1974 and 1976 works, Stephen Hawking proved that black holes slowly emit particles in the thermal spectrum, gradually evaporating. Qualitatively, but not very correctly, this process can be described as follows. Due to the Heisenberg uncertainty principle, particle fields can “borrow” energy for a moment and generate a virtual pair of antiparticle particles, which in normal external conditions will immediately self-destruct, returning the energy back. However, near the event horizon, the tidal forces are so large that they can pull one of the virtual particles inside the black hole, and the other particle will fly away. In this case, due to the strong gravitational field, the particles that fell into the black hole, on average, will have negative energy, reducing the mass, charge and spin of the black hole, and the radiation that reached the outside observer – the so-called Hawking radiation – will be in thermal state, which depends only on the mass, charge and spin of the black hole at the time of radiation of the particle. You can find more information about Hawking radiation in our blog “What do Hawking radiation have to do with the Unru effect?” and materials “Chronicler of Time”.
Based on the assumption that black hole radiation is indeed exclusively thermal in nature and there are no other channels of information output, the hair loss theorem was formulated: two different black holes with the same mass, charge and spin do not differ from each other. Shortly after the discovery of radiation in black holes, Hawking formulated the paradox of the disappearance of information in a black hole, the essence of which is that a black hole will gradually evaporate, getting rid of previously found bodies, along with information about them. From the point of view of quantum mechanics, the following happens: the object got into a black hole in the pure state, and he can leave it only in a mixed state in the form of Hawking thermal radiation – this process is not unitary, and the unitarity of evolution is considered one of the most important postulates of quantum mechanics (with the help of a unitary operator it is possible to carry out the evolution of the quantum state back and forth in time).
Because the paradox is based on assumptions that do not take into account the quantum nature of space-time and the features of old black holes, some scientists argue that Hawking’s calculations are sufficient to add quantum corrections that carry information about the internal state of the black hole, while others agree. that information leaves a black hole in the later stages of her life. In addition, many other solutions to the paradox are known. For example, one study claims that information crosses the horizon in the form of correlations between particles in Hawking radiation particles, and in 2016 Strominger, Perry and Hawking published an article according to which information leaves a black hole through low-energy particles without mass – “soft hair” ». (Photons or gravitons). We talked in detail about the latest work with physicist Emil Ahmedov.
A new step in solving the information paradox was taken by a team of scientists led by Xavier Calmet from the University of Sussex and Stephen DH Hsu from the University of Michigan. In the first paper, the scientists proved the unambiguous correspondence between the state of the gravitational field outside the black hole and the state of matter inside it, and in the second they deduced the unitarity of black hole evaporation.
In the first of these studies, scientists demonstrated the dependence of the graviton field on the energy of the inner state of a black hole, and explained why each value of black hole energy corresponds to a specific quantum state that carries much more information than black hole mass, charge and spin. Then physicists showed how information is encoded in gravitons. It turned out that the corrections to Newton’s potential arising from Einstein’s equation with quantum corrections depend on the internal structure of the black hole. In other words, two black holes of the same mass, but with different distribution of matter inside, give different corrections to the gravitational potential, and hence the states of gravitons on the other side of the event horizon will be different. This means that a black hole has “quantum hair”.
In the second article, physicists, based on the conclusions of the first work, explain how the state of gravitons affects Hawking radiation. Since the external gravitational field at the quantum level depends on the internal state of the black hole, the amplitude of the radiation of the sublibating particle will also depend on the state of the black hole. The authors argue that this dependence is significant and makes the mixed state of Hawking radiation pure, returning unitarity to evaporation. Meanwhile, when a particle radiates, the state of the external gravitational field changes, as does the internal state of the black hole, so the amplitude of the next particle’s radiation will depend on the new state of the black hole, and so on until the black hole evaporates completely. Ultimately, the total state of the radiation will be a superposition of the pure states that depend on the initial state of the black hole. From this state, the initial state of a black hole can be obtained by turning time (ie, by some unitary operator), which was impossible without taking into account quantum corrections.
And although, according to the authors, the influence of the internal state of the black hole on Hawking radiation is significant, in the leading order it remains thermal. Unfortunately, at this stage of technology it is impossible to verify this experimentally, because the temperature of Hawking radiation for a black hole of the mass of the sun is one hundred million times lower than the temperature of relic radiation. To study Hawking radiation in practice, scientists are looking for analogues of this phenomenon in more accessible models. In 2019, for example, physicists from Israel and Mexico received an optical analogue of Hawking radiation using the Kerr effect.