In a fully quantum view, whether you adopt

- the Chapline view - horizon as a quantum critical-opalescent condensate - see gr-qc/0012094 or
- the Cerf-Adami view - non-equilibrium thermodynamics of quantum information conditional entropy - see quant-ph/9904006 or
- the superstring fuzzball view (mentioned by Lubos Motl) of Mathur et al - see hep-th/0401115

the end result is the same: the area = entropy relationship is not fundamental, and there is no information paradox, so that it seems to me that the t'Hooft-Susskind hologram program is not something that is part of a fundamental quantum theory, but only something that at most appears to be approximately correct from a semi-classical viewpoint.

**George Chapline, E. Hohfeld, R. B.
Laughlin, and D. I. Santiago**, in their paper gr-qc/0012094
entitled **Quantum Phase Transitions and the Breakdown of Classical
General Relativity**, say:

"... It is proposed thatthe event horizon of a black hole is a quantum phase transition of the vacuum of space-time analogous to the liquid-vaporcritical pointof a bose fluid. ...1. The equations of classical general relativity outside the black hole are obeyed everywhere except the critical surface.2. At the critical surface the vacuum of space-time reorganizes itself so as to keep global time defined.

3. The local properties of the vacuum just inside the critical surface are indistinguishable from those just outside.

4. There are no scales other than the mass.

5. The topology is consistent with the collapse of ordinary matter. ...

The equations of classical general relativity remain valid arbitrarily close to the horizon yet fail there through the divergence of a characteristic coherence length ...

The metric inside the event horizon is different from that predicted by classical general relativity and may be de Sitter space. ...

Regardless of whether it the event horizon corresponds to a first- or second-order phase transition, identifying the space-time of a black hole as a quantum ground state resolves the information paradox.

The horizon does not destroy quantum information but rather makes entropy the same way black paint does, i.e. by scattering the energy into a thermodynamically large number of degrees of freedom. ...

The deviations from classical behavior lead to distinct spectroscopic and bolometric signatures that can, in principle, be observed at large distances from the black hole. ...

Insofar as string theory predicts something else, the two theories can be distinguished from each other by experiment. ...".

Note that the version of string theory of Mathur et al may not make predictions different from those of Chapline et al.

The ideas of **Chapline et al** are further discussed by
**Walid Abou Salem**, in a
paper entitled **Is Gravity Emergent?** where he says:

"... G. Chapline proposes that macroscopic space-time emerges from microscopic fluctuations ... He suggests that the condensate wave function for the three dimensional anyonic superfluid can be reinterpreted as a quantum wave function for space-time. Just like electrodynamics is represented on the quantum level by coherent states of photons,space-time can be represented as a coherent sum of nonlinear gravitons. ...

the constructed space-time wave function has a long range off-diagonal order, and hence one expects a universe described by it to have quantum effects on the macroscopic scale. One such possible effect is that the event horizon of a black hole differs from the one predicted by classical general relativity whereby space-time vacuum rearranges itself in such a manner that time is universally defined ...Now how does all of that relate to black holes?

Assume that

the event horizon is a quantum liquid-vapour transition. The equations of classical general relativity outside the black hole are obeyed except at the event horizon.At the latter, space-time reorganizes itself in such a way that a universal time is still defined.

Locally, the properties of the vacuum are the same inside and outside of the vacuum.

...

one needs a nonzero cosmological constant inside the black hole, and Einstein's equations are modified inside the black hole...In this picture, the break down of relativity must be observed experimentally as the spontaneous decay of bosons such as photons.

If the phase transition is first order, the excitations are unstable, and they will generate a non-uniform metric with sharp jumps.

Irrespective whether it is a first or second phase order transition, quantum information isn't destroyed by the black hole. Instead, energy is scattered as if by dark paint....".

In their paper quant-ph/9904006
entitled "**Prolegomena to a Non-Equilibrium Quantum Statistical
Mechanics**" **Cerf and Adami** say:

"... if the Bekenstein-Hawking entropy could be understood in terms of a conditional entropy ... entropy flow from the black hole to the outside via the formation of virtual pairs is understood easily, as the member of the pair that crosses the horizon not only has negative energy but also negative conditional entropy. As a conditional entropy can become as negative as the marginal entropy of the system it is a part of, we can circumvent the argument that "the black hole cannot store the information until the end because it runs out of quantum states", because the radiation could "borrow" as much entropy as necessary from the black hole until the horizon has disappeared. ... It is not inconceivable ... that a quantum statistical information theory extended to curved space-time would reveal ... that the Bekenstein-Hawking entropy is in fact conditional ...".

**The Cerf-Adami "quantum information theory" on "curved
spacetime" may be just another way of describing the "critical
surface" at which "the vacuum of space-time reorganizes itself so as
to keep global time defined", according to Chapline et al.**

**Mathur et al** say in hep-th/0401115:

"... the 'information paradox': Hawking radiation from the hole is created by the progressive dilation of vacuum modes near the horizon, and if the geometry here is determined only by the above conserved quantities ... mass, charge and angular momentum ... then the radiation will carry no details of the matter which went in to make the hole. We thus get a violation of the unitarity of quantum mechanics ...we propose that

the interior of the horizon is not described by the conventional picture ... where we have 'empty space with a central singularity'.

Rather the differences between the ... state information is distributed throughout the 'fuzzball' ... interior of the 'horizon'... the horizon is just the boundary of the region where the typical states differ from each other. ...... consider the ... microstates that give the entropy of a black hole.

Some attempts to locate the 'hair' have looked for small perturbations near the horizon ... Other approaches would suggest that the microstates differ only within a planck distance of the central singularity. In either case each microstate looks pretty much like ... a horizon with an area ... But if each of the ... microstates has such a horizon, then it must itself represent different states. This makes no sense, since we wanted the microstates to explain the entropy, not have further entropy themselves. We conclude that the ... microstates should have no horizons individually - the notion of a horizon should arise only after 'coarse-graining' over these microstates. ... If we 'coarse-grain' by drawing a boundary to enclose the region where these geometries differ significantly from each other ... then from the area A of this boundary we find S = A / 4G ... Thus the Bekenstein 'area entropy' arises directly as a 'coarse-graining over hair'. ...

... Hawking's calculation of radiation showing information loss is so robust because it uses no details of the physics at the planck scale.

Resolving the information paradox thus needs an explicit nonlocality over macroscopic distances. ... thus the interior of the horizon is not just 'empty space with a central singularity'. This makes it possible for radiation from the hole to pick up information from the 'hair' and avoid the information paradox. ... It is possible that infalling matter falls straight through the 'fuzzball' towards r = 0 (as if it were falling through a conventional horizon), but over the Hawking evaporation time information is transferred to the 'light fractional modes' and into the radiation. ...".

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