‘Quantum hair’ helps solve the paradox of the disappearance of information in a black hole

(ORDO NEWS) — A group of physicists from three countries proposed a solution to the paradox of the disappearance of information in a black hole using “quantum hair”: the matter inside the black hole at the quantum level encodes information in an external gravitational field, and this, in turn, is reflected in the Hawking radiation.

In the first paper, published in the journal Physical Review Letters, physicists proved the dependence of the states of gravitons outside a black hole on the state and distribution of matter inside it. In a second paper, published in the journal Physics Letters B, the scientists explained how this connection drives the black hole’s unitary evaporation.

Quantum hair helps solve the paradox of the disappearance of information in a black hole

In his 1974 and 1976 papers, Stephen Hawking provided evidence that black holes slowly emit particles in the thermal spectrum as they gradually evaporate. Qualitatively, but not quite correctly, this process can be described as follows.

Because of the Heisenberg uncertainty principle, particle fields can “borrow” energy for a moment and generate a virtual particle-antiparticle pair, which, under normal external conditions, will immediately self-destruct, returning the energy back.

However, near the event horizon, tidal forces are so strong that they can pull one of the virtual particles into the black hole, and the other particle will fly away.

At the same time, due to the strong gravitational field, the particles that fell into the black hole will on average have negative energy, reducing the mass, charge and spin of the black hole, and the radiation reaching the external observer – the so-called Hawking radiation – will be in a thermal state, which depends only on the mass, charge and spin of the black hole at the moment the particle is emitted.

You can find more precise information about Hawking radiation in our blog “What do Hawking radiation and the Unruh effect have in common?” and the material “Chronicler of Time”.

Based on the assumption that the radiation of a black hole really has an exclusively thermal nature and there are no other channels for the release of information, the hairless theorem was formulated: two different black holes with the same mass, charge and spin are indistinguishable from each other.

Shortly after the discovery of radiation from black holes, Hawking formulated the paradox of the disappearance of information in a black hole, the essence of which is that the black hole will gradually evaporate, getting rid of the bodies that previously fell into it along with information about them.

From the point of view of quantum mechanics, the following happens: the object entered the black hole in a pure state, and it can leave it only in a mixed state in the form of thermal Hawking radiation – such a process is not unitary,

Since the conclusion of 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 it is enough to add quantum corrections to Hawking’s calculations, which will carry information about the internal state of the black hole, while others converge on that information leaves the black hole in the last stages of its life.

In addition, many other solutions to the paradox are known. For example, one study claims that information crosses the event horizon in the form of correlations between particles in Hawking radiation, and in 2016 Strominger, Perry and Hawking released a paper according to which information leaves a black hole through low-energy massless particles – “soft hair” (photons or gravitons). We discussed the latest work in detail with the physicist Emil Akhmedov.

A new step in resolving the information paradox was made by a group of scientists led by Xavier Calmet (Xavier Calmet) from the University of Sussex and Stephen Hsu (Stephen DH Hsu) from the University of Michigan.

In the first article, scientists proved a one-to-one 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 from this the unitarity of the black hole evaporation – the final state of Hawking radiation will be in a superposition of pure states depending on the internal state of the black hole.

In the first of the mentioned works, scientists demonstrated the dependence of the state of the graviton field on the energy of the internal state of the black hole, and also explained why each value of the energy of the black hole corresponds to a specific quantum state, which carries much more information than the mass, charge and spin of the black hole.

Then physicists showed how information is encoded in gravitons. It turned out that the corrections to the Newton potential that arise from the quantum-corrected Einstein equation depend on the internal structure of the black hole.

In other words, two black holes of the same mass, but with a different distribution of matter inside, give different corrections to the gravitational potential, which means that the states of gravitons on the other side of the event horizon will be different for them. This means that the black hole has “quantum hair”.

In the second article, physicists, based on the findings 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 radiation amplitude of the particle in the subleading order 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, restoring unitarity to evaporation.

Meanwhile, when a particle is emitted, the state of the external gravitational field changes, as does the internal state of the black hole, which means that the radiation amplitude of the next particle will depend on the new state of the black hole, and so on, until the black hole completely evaporates.

Ultimately, the total radiation state will be a superposition of pure states, depending on the initial state of the black hole. From this state, by time reversal (that is, by some unitary operator), it is possible to obtain the initial state of the black hole, which was impossible without quantum corrections.

And although, according to the authors, the influence of the internal state of a black hole on Hawking radiation is significant, in the leading order it remains thermal.

Alas, at this stage in the development of technology, it is not possible to verify this experimentally, since 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 the cosmic microwave background radiation.

In order to somehow investigate 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 obtained an optical analogue of Hawking radiation using the Kerr effect.


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