Quanta magazine claims that there is progress in the black hole information paradox

https://www.quantamagazine.org/the-black-hole-information-paradox-comes-to-an-end-20201029/ 

The Quanta article says that a group of researchers first considered black hole evaporation in the context of the conjectured AdS/CFT duality. Then they were able to eliminate the link to AdS/CFT using path integrals.

The Wikipedia page:

https://en.wikipedia.org/wiki/Black_hole_information_paradox

discusses the work of Penington et al.

The claims remind us of the announcement by Stephen Hawking in 2004 that he is able to recover the information which has fallen into a black hole, using Euclidean path integrals:

https://arxiv.org/abs/hep-th/0507171

Does Hawking radiation exist? Vladimir Belinski has claimed that the calculation by Hawking is erroneous. In this blog we have raised questions about conservation of momentum if we assume that the black hole horizon radiates photons. A photon carries away a momentum p. What, and how, could absorb the opposite momentum -p?

As far as we know, no one has refuted the criticism by Belinski, and no one has shown a mechanism which would conserve momentum.

What about the claims that we can use a path integral and show that the information falling toward the black hole horizon is preserved, after all?

Let us assume that a macroscopic black hole forms, and it devours and crushes a large part of the wave function, or, of the path integral.

In quantum mechanics, one cannot simply throw away a part of the wave function or a path integral. It is a strange claim that the remaining part would be equivalent to the entire original wave function.

The horizon of a black hole is classically a one-way surface. Information can fall in, but can never come back.

Let us do a thought experiment: instead of a black hole, we have a horizon which leads to a wormhole, and the wormhole opens into a white hole in some other part of our universe. If we claim that the horizon necessarily returns back the information which has passed by, how do we explain that the same information ends up to another part of our universe? This is against the "no-copying" principle of quantum mechanics.

People who claim that a black hole horizon must necessarily give up the information it has devoured, kind of claim that the universe behind the horizon is "inferior" to our own universe. They think that the entropy should be calculated based on what is on our side of the horizon, and we should ignore what is behind the horizon. That does not sound like a reasonable assumption. Why would the other side be inferior to our side?

The Quanta magazine article points at the large number of assumptions and idealizations which Penington et al. use.  That is a weakness in the new work.

Does a system eventually radiate all its entropy out in an asymptotic Minkowski space?

Consider a block of glass. It is amorphic material and contains quite a lot of entropy. When a very long time passes, glass becomes crystallized, and its entropy dramatically decreases. After an immense time, the block of glass will assume a state of the lowest energy. That state might be one spherical crystal - spherical because of the gravitational attraction.

Hawking, Bekenstein, and others probably had this phenomenon in their mind when they conjectured that a black hole horizon must necessarily have a non-zero temperature since it encloses a lot of entropy inside.

But let us think about the wormhole example above. If we throw a block of glass through the horizon, the entropy of the glass will slowly seep out into the new part of the universe where the block of glass ends up. There is no obvious reason why the entropy should climb up the wormhole to the wrong direction and magically return back from the horizon.

If we take macroscopic one-way surfaces seriously, then the entropy will remain behind the surface. If it is a wormhole, then the entropy will pop out of a white hole. If the surface is a black hole horizon, then the entropy will remain confined behind the horizon.

Let us compare a block of glass to a black hole horizon. An observer can see that the atoms are in a disorder in the glass. He sees that there is a lot of entropy.

But if a black hole horizon rapidly becomes an ideal geometric object, and essentially black, too, then an outside observer does not see a lot of entropy there. He does know that the horizon devoured a lot of entropy, but he can no longer directly observe the disorder. This is in contrast to a block of glass. 

Do cosmological horizons somehow radiate back the entropy in the galaxies that they devoured?

https://en.wikipedia.org/wiki/Cosmological_horizon

In an accelerating expansion of an FLRW universe, galaxies eventually disappear behind a cosmological horizon.

If horizons generally would give back the entropy which they have devoured, would a cosmological horizon eventually return us all the information in the galaxies which it swallowed? That seems implausible.