Black Holes Are Surrounded By A "Wall Of Fire"

Since the beginning of the 20th century, black holes have aroused the interest of physicists. While  some of their physical characteristics have a solid theoretical description, others  are still nebulous. This is particularly the case for the horizon of  events and the question of what happens once the information gets into it.

In 1976, the physicist Stephen Hawking highlights the contradiction between general relativity and quantum mechanics concerning information within black holes. In fact, on the one hand, general relativity postulates that all information passing the horizon of a black hole is definitely trapped there. However, under the effect of Hawking radiation, the black hole eventually evaporates, the information is then permanently lost.

On the other hand, quantum mechanics postulates the reversibility and unity of the quantum states, necessarily implying the conservation of information. Since then, physicists have constantly sought solutions to the paradox of information.

A solution to the paradox of information: the complementarity of black holes

In 1993, physicists Leonard Susskind and Larus Thorlacius develop a hypothesis (see image below) potentially solving the paradox of information: the complementarity of black holes. Susskind describes this hypothesis as follows: " The information that comes into contact with the horizon of the events of the black hole is both reflected by the horizon and at the same time trapped by the horizon; however, no observer can confirm these two issues simultaneously . " The term "complementarity" was used for the first time concerning the wave-particle duality of a particle; the authors have reused this term to apply this analogy to black holes.

This solution includes two hypotheses, depending on whether an observer is viewed from outside the horizon or from the point of view of an observer crossing the horizon. For an outside observer, the information coming into contact with the horizon is absorbed by a membrane surrounding the horizon on the Planck scale and then re-emitted via the Hawking radiation. On the other hand, an observer crossing the horizon would not notice anything particular, it would simply fall with the information towards the singularity.

Illustration simplifying the theory of the complementarity of black holes. A) An elephant approaches a black hole. B) Observer A (outside) sees the elephant moving closer and closer to the horizon, while observer B (inside) sees the elephant pass through. C) The observer A sees the elephant being radiated opposite the horizon, whereas the observer B sees the elephant falling towards the singularity. Credits: Universe-review.ca

Although correctly solving the information paradox, Susskind and Thorlacius's theory is not devoid of problems. Indeed, it contradicts a key principle of quantum mechanics: the monogamy of entanglement.

Complementarity of black holes and monogamy of entanglement

Let's first briefly recall what Hawking's radiation is. According to Heisenberg's principle of indeterminacy on energy and time, the quantum vacuum fluctuates continuously. From these quantum fluctuations arise virtual particle-antiparticle pairs that annihilate almost immediately after their appearance. However, near a black hole the gravitational field is so intense that it separates the particle-antiparticle pairs before annihilation. One particle is absorbed by the black hole, while the other is emitted by escaping from its attraction.

According to quantum field theory (the theory describing the behavior of fundamental interactions), Hawking radiation produces an entangled system between the absorbed particle and the emitted particle. But that's not all. Indeed, in 1993, the physicist Don Page, in collaboration with Susskind, published works demonstrating that the emitted particle, in addition to being entangled with the absorbed particle, is also entangled with all the information previously emitted by Hawking radiation. . Thus, in the case of the black hole complementarity theory, Hawking's re-radiated information is entangled both with the definitively absorbed information and with all the information previously radiated before it.

However, there is a fundamental principle in quantum mechanics called "monogamy of entanglement". This principle asserts that it is impossible for a quantum system (for example a particle) to be entangled simultaneously with two systems independent of each other. In other words, applied to the Hawking radiation, it is forbidden for the emitted particle to be simultaneously entangled with the absorbed particle and with the information previously emitted.

Diagram illustrating the principle of monogamy of entanglement: it is forbidden for a particle to be fully entangled with two other other independent particles. Credits: Universe-review.ca

A "wall of fire" as a solution to the problem of monogamy of entanglement

In order to solve this contradiction, the physicists D. Marolf, J. Polchinski, A. Almheiri and J. Sully publish in July 2012 a theory entitled "black hole firewall", literally "wall of fire of the black hole".

In this theory, physicists propose the idea that during the separation of the absorbed particle and the emitted particle, the quantum entanglement connecting the two particles breaks down immediately. During this break, a phenomenal amount of energy would be released around the horizon. In this regard, Polchinski explains that " it is an extremely violent process, like breaking the bonds between molecules, it releases a large amount of energy ". He goes on to say that " the horizon of events would then literally be a ring of fire that would burn anyone who would pass through ".

Representation of the "firewall" theory. During Hawking radiation, the entanglement between the emitted particle and the absorbed particle is broken, releasing a huge amount of energy and forming a "fire wall" around the black hole. The emitted particle, however, retains its entanglement with all previously issued information. Credits: Nature

Thus, the continual breaking of the entanglement of all particle-emitted particle-absorbed systems would result in the permanent formation, at Planck's scale, of a chaotic maelstrom of ultra-energetic particles constituting a real "firewall" all around of the event horizon. To cross this wall of fire would result in an immediate and violent incineration. It should be noted, however, that from the point of view of an outside observer, the wall of fire is perfectly invisible.

If such a wall of fire exists, then it should leave gravitational traces during important cosmological phenomena such as the fusion of two black holes. In this case, an impression of the two walls of fire would be present in the gravitational waves emitted during the fusion. Such traces were sought in the first data collected by LIGO in 2016; however, the amount of data was insufficient to confirm or rigorously deny their existence. In the coming years, with the accumulation of new data, physicists should be able to provide a definitive answer to this hypothesis.

This theory thus makes it possible to complete the theory of the complementarity of black holes by preserving the monogamy of entanglement. However, to be viable, this hypothesis must sacrifice a fundamental postulate of general relativity: the principle of equivalence. By virtue of this principle, an observer crossing the horizon of a black hole should not feel anything. This is why the authors, at the end of their publication, leave a choice to the scientific community: to accept the hypothesis of the "firewall" and to abandon the principle of equivalence and thus to a part of the general relativity, or to reject this hypothesis and adhere to the loss of information and thus give up some of the quantum mechanics.

Sources: Nature , arXig.org ( 1 & 2 )