What is the information loss problem in black holes?

This is the first photograph of a black hole  taken in April 2019 with the Event Horizon Telescope of the supermassive black hole in M87.

A black hole is a massive star which have collapsed under its own weight into a compact region of space.
The force of gravity around a black hole is so extreme that even photons (the particles of light) which travel at the speed of light can not escape once they have crossed the so-called event horizon surrounding the black hole.
Thus, black holes are really holes in space (since matter fall into them) which are really black (there is no possibility of escape).
This is the picture of classical black holes provided by Einstein general theory of relativity.
But in 1974 Hawking showed that black holes are really quantum objects which can emit radiation (the so-called Hawking radiation).
Indeed, a black does not really exist in vacuum but in fact it is continuously interacting with fields of particles and radiations which permeate spacetime.
In other words, the space surrounding a black hole is filled with  virtual particles which pop in and out of existence (by the Heisenberg uncertainty principle of quantum mechanics) in the form of matter-antimatter pairs.
These pairs annihilate almost immediately.
But around the event horizon of the black hole it could happen that a pair of particle-antiparticle is created for a brief short of time but before they can annihilate  the force of gravity of the black hole pulls one of them inside the black hole whereas the other scatter off away from the black hole towards infinity.
The absorbed particle is the lost qbit (or quantum bit) of information.
And the scattered particle (seen by an observer located outside the black hole at spatial infinity) is the Hawking particle.
The lost bit falling inside the black hole has negative energy causing thus the mass of the black hole to decrease and as a consequence the black hole is actually evaporating by the process of Hawking radiation.
The loss of information problem is the statement that the created pair of particle-antiparticle is found in a quantum pure state whereas the Hawking radiation constituted of all Hawking particles is found in a thermal mixed state.
The mixed state lacks all quantum correlations encoded into the original pure state and hence we have here a case of a pure state evolving in time to a mixed state which is impossible by the Schrodinger equation.
We say that unitarity is lost and we have loss of information. Which is a state of affair not accepted by the majority in the physics community.

A precise formulation of this problem is given by the AMPS (Almheiri, Marolf, Polchinski, Sully)  firewall paradox which shows among other things that black hole complementarity is not sufficient.
In my own view the solution of this problem is that there is no information loss and that the black hole starts spitting out its information back out at an accelerated rate when it becomes maximally entangled with its Hawking radiation at the the so-called Page time (the time at which half of the black has evaporated).

This solution should in fact go through the following three stages:

- The ER=EPR conjecture due to Maldacena and Susskind which states that the black hole and its Hawking radiation are maximally entangled with each other. And that the maximal entanglement (that is the Einstein-Podolsky-Rosen or EPR  entanglement) between any Hawking particle and its lost quantum bit which went inside the black hole is given by Einstein-Rosen or ER wormehole or bridge. We get thus an octopus structure for entanglement.

- The ER=EPR conjecture is actually based on the hypothesis that the smooth geometry of spacetime is woven solely from particle entanglement.  We say that spacetime emerges from quantum entanglement. This more fundamental hypothesis is due for example to Van Raamsdonk.

- The hypothesis that spacetime is an emergent concept from the more fundamental quantum entanglement is itself based on the celebrated AdS/CFT conjecture due to Maldacena which states that quantum gravity in certain spacetime geometries is completely describable in terms of ordinary quantum fields (with conformal symmetry) in lower dimensions.

We hope we can come back to these points in more detail in the future.

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