The BH information paradox arises from people who do not know that the fine grained (von Neumann) entropy is conserved, while the coarse grained one increases. After all, entropy is entropy, isn't it? NO, NO, NO, you fool.

Th. M. Nieuwenhuizen then what happens to the information encoded in that entropy when matter falls into a black hole?

It is conserved, and correlated with the entropy before the infalll, and with the Hawking radiation. Even in condensed matter systems you could not show the constancy of the fine-grained entropy by measurments. Likewise, a Dyson sphere would never achieve it. So it is not a physical question. When you coarse grain, for instance by considering the Hawking radiation as thermal, you get an increasing entropy.

“Can quantum theory of gravity solve the black hole information paradox?”

- real quantum gravity theory by no means can solve “the black hole information paradox” for the quite evident reason – since this “paradox”, which follows from the “GR black holes” models, where the black holes are some “holes in Matter’s spacetime” because of the spacetime on the “black hole event horizon” surface is infinitely “curved”,

- simply fundamentally cannot, and so doesn’t, exist.

As that is rigorously scientifically shown in the Shevchenko-Tokarevsky’s informational physical model , two main papers are

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics, and

https://www.researchgate.net/publication/355361749_The_informational_physical_model_and_fundamental_problems_in_physics

- Matter’s spacetime is the fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (cτ,X,Y,Z,g,w,e,s,ct), which fundamentally cannot be transformed, i.e. “contracted”, “dilated”, “curved”, “warped” , etc., by anything in Matter

- and fundamentally cannot affect anything in Matter; the spacetime is really nothing else than some empty container, where everything in Matter exists and happens.

Though yeah, “black holes” are indeed extremely exotic, and indeed really rather black, material objects, and so the wording “black hole” in this case is well suitable.

More about what are “black holes” see the SS&VT initial cosmological model in section “Cosmology” of the 2-nd link above, what is [including quantum] Gravity, which fundamentally is nothing else than some fundamental Nature force, see the SS&VT 2007 initial model of Gravity and Electric Forces in

https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces, including in this paper black holes are considered as well.

If briefly – “black holes” are some material objects, the matter in which is in unknown till now, however by no means mystic, state, that is a next state after “usual matter”, “white dwarf”, and “neutron star” states,

- at that fundamentally no any singularities exist on the black holes “event horizons” surfaces, and, say, on SMBHs’ event horizons conditions and parameters of matter are quite tolerant. Etc., more see the links, though note here also that, as that quite rigorously shown in the SS&VT Electric and Gravity Forces models above and in the initial model of Nuclear Force [https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force], all Forces exist and act by the one universal scheme;

- so it seems that the matter’s “black hole state” can be not too exotic state.

Cheers

Dear Subash Bhandari

There are 2 universal conservation laws: energy and momentum. The latter is about a local amount of energy and its direction (the vector). The energy is already part of the law of conservation of energy – every quantum of energy has momentum too – thus the 2 universal conservation laws are about energy and vectors.

But energy is generated by the universal electric field and vectors represent the corresponding magnetic field (together termed “electromagnetic field”). I can precise the universal electric field as a topological field (3D) while the vectors of the magnetic field are 1 dimensional (a vector is not “tangible” in physical reality, only its influence).

One can argue that there are more basic quantum fields, inclusive the proposed quantum gravitational field. But these fields are transformations of the electromagnetic field (for example the 2011 paper of Eric Verlinde about Newtonian gravity as an emergent force field). It doesn’t matter what kind of cosmological model you prefer but every model has a period that there was no matter in the universe. Thus everywhere in the universe the Higgs field was perfectly flat and there was no gravity too. The only variables were the amplitudes of the electromagnetic field “in vacuum space”.

If all the variables in the universe – actually the dynamical part of the universe – is covered by the conservation of the properties of the electromagnetic field, where is the information? Information isn’t static thus the only possibility is that the term “information” is a concept that is synonymous with the electromagnetic field.

But there exists no “electromagnetic paradox” in relation to a black hole. No matter the size of a black hole, within its boundary (event horizon) there is the electric field and decreased scalars of the Higgs field. But the basic quantum fields are everywhere in the whole universe (QFT) thus nothing is “locked” inside a black hole. In mathematical physics (models of the properties of quantized space) a black hole is just a phenomenon, not even a “weird” phenomenon.

Your question not only envelopes “the paradox” but also the proposed theory of quantum gravity. I don’t see a direct relation although it is clear that our present main theories of the force of gravitation – curved spacetime, Newtonian gravity, MOND – are approximations.

Personally I have the opinion that (quantum) gravity is Newtonian gravity as a push force from vacuum space around (thus a vector force with an instantaneous influence that is super positioned on the vectors of the magnetic field). It is about the vectorized scalars of the Higgs field in vacuum space because the matter object envelopes one or more decreased scalars of the Higgs field). Anyway, this doesn’t solve the proposed “information paradox” because there is no reasonable paradox. We have “invented” a paradox because there is too much focus on competition instead that we focus on the foundations of physics (and mathematics).

With kind regards, Sydney

The event horizon of a black hole is not a singularity and the Kretschmann curvature scalar is finite there. I found exact solutions with normal matter:

Preprint Exact solutions for black holes with a smooth quantum core

Dear Th. M. Nieuwenhuizen

I have scanned your paper (reading everything is too difficult because I use another conceptual framework). Your paper is really interesting and if I have interpreted your general concept of a black hole well – and I agree with this concept – it is some kind of an enormous particle (without singularity).

Your theoretical method is limited to non-rotating black holes. I am aware of the conceptual difficulties to transform the used method into one that can describe the dynamical model. Besides that, nowadays we are confronted with the electromagnetic field as a rest frame – because of the CMBR dipole – thus spherical models are simplifications of the propagation of some kind of a “swirl” of concentrated energy in/by the electromagnetic field.

Probably a black hole is like a rotating oblate spheroid because this shape shows a more pronounced “cut off” for accretion disks and “stimulate” the creation of the 2 axial jets. If the ratio of an oblate spheroid black hole is e.g. about 9 : 11 the gravitational influence at the “poles” is ≈ 50% of the gravitational influence at the “equator”. However, this is only true if we propose that the force of gravitation is created by the decrease of local scalars of the Higgs field (“rest mass”). It is evidently that the model of a black hole with a singlarity inside cannot have the shape of a oblate spheroid.

With kind regards, Sydney

Problem is that right now we are in possession of no fully valid Q_theory of gravity ............

Th. M. Nieuwenhuizen,

if you are interseted, I have in my first book (in my profile) given another description of black holes, namely of those in the centre of the galaxies.

Hans Gennow : Extension of cored BHs to the rotating case seems possible, I made a few steps, but for now it looks ugly.

Unlike white dwarfs and neutron stars, black holes do not require matter for construction -- black holes are pure geometry. According to the classical definition, black holes are global vacuum solutions of Einstein gravity that are asymptotically flat (like Minkowski space-time) and have an event horizon. These solutions were found by Karl Schwarzschild in 1916 as static black holes and by Roy Kerr in 1965 as rotating black holes. They did not appear in astronomy as X-ray sources until the 1970s : but again , black holes are pure geometry.

Reza Sanaye Yes, this is the standard viewpoint. The "pure geometry" BHs have a singularity, which is pretty awkward; for obvious reasons, it is not tested in practice. Focussing too much in the Schwarzschild case is misleading, since its inner horizon lies at the singularity, so a special limit. I have proposed smooth exact solutions, which do not have singularties. Such may be the ones realized in the cosmos.

Reza Sanaye,

your black holes are real stuff. Forget about Einstein, he know nothing.

They consists of particles, what else?

Hans Gennow "They consist of particles. What else?" Vacuum energy does the job, see my arXiv:2302.14653 Exact solutions for black holes with a smooth quantum core

Th. M. Nieuwenhuizen,

I could not find your article, what session?

I just mention that the cores of the galaxies I build is due to a quantum mechanical process. The result is deeply bound particle-antiparticle pairs. The binding prevents them from annihilating (my first book in my profile).

Th. M. Nieuwenhuizen

Hans Gennow

I appreciate your depth of knowledge on BHs . Thanks for your posts . My strong guess is that we three ought to work more closely on BHs issues .

First ,Lets talk of Event horizon :

Hawking proposed a solution to this paradox: Black holes have no event horizon and therefore do not destroy information.

"The absence of event horizons means that there are no black holes in the sense of systems from which light cannot escape," Hawking wrote in the paper, which he published online Jan. 22, 2014. It was based on a talk he had given the previous August at a workshop at the Kavli Institute for Theoretical Physics in Santa Barbara, California.

Hawking hypothesized that black holes have an "apparent horizon" that traps matter and energy only temporarily. Both could eventually escape in the form of radiation. This outgoing radiation contains all the original information about what passed the apparent horizon, but in a significantly different form. Since the outgoing information is scrambled, Hawking writes, there is no practical way to reconstruct its original form. These scrambles occur because the apparent horizon is chaotic - a bit like the weather on Earth.

We can't reconstruct what fell into the black hole from the information leaving it, he writes, just "as you can't predict the weather more than a few days in advance."

Next issue are the Firewalls :

Hawking's arguments against event horizons also seem to eliminate the so-called firewalls - glowing hot belts of radiation that some scientists say exist at or near the event horizon. However, this theory is quite controversial.

To understand the implications of this revision, it helps to recall Hawking's conclusion about black holes, which he reached decades ago: black holes are not perfectly "black" at all. Instead, they emit radiation just beyond their event horizon. The energy of their gravitational field causes particle pairs to form in the surrounding vacuum.

Over time, the black holes lose mass due to the generation of this so-called Hawking radiation or, theoretically, could even disappear altogether.

According to this theory, the particles of the pairs should be entangled with each other. This means that the particles are connected regardless of the distance between them. One particle of the pair falls into the black hole while the other escapes.

Recent analysis suggests that any particle that leaves the black hole must also be entangled with any other particle that has already left the black hole. This contradicts an extensively tested principle of quantum physics, which states that such quantum entanglement is always monogamous - it exists exclusively between two particles from the moment of their creation.

Since no particle can have two entanglements at the same time, theoretically one of these entanglements must be cancelled. This releases large amounts of energy, which form the firewall.

Firewalls follow the rules of quantum physics and therefore solve the black hole problem with respect to quantum entanglement. However, they raise another problem by contradicting Einstein's well-tested equivalence principle, according to which the crossing of the event horizon of a black hole should be an inconspicuous process. A hypothetical astronaut crossing the event horizon should not even notice it. However, if there were a firewall, the astronaut would instantly burn up.