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I am new, not have expert level knowledge. But I have studied about black hole information paradox. The black hole doesn't kept any information which passes event horizon. Which can break physics. Is there any theory about Information Paradox, to resolve it.

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  • $\begingroup$ The black hole information paradox is solved now, and we understand the physics of it.” The quantum hair theorem claims to resolve the paradox by bridging the gap between general relativity and quantum mechanics using a new mathematical formulation. $\endgroup$ Commented Aug 16, 2023 at 8:44
  • $\begingroup$ Can you explain what is quantum hair theorem $\endgroup$
    – user375123
    Commented Aug 16, 2023 at 9:07
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    $\begingroup$ No theory so far has been able to resolve the information paradox. It is an active area of research. $\endgroup$
    – Prahar
    Commented Aug 16, 2023 at 10:13
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    $\begingroup$ Is my question has any mistake?????????????? $\endgroup$
    – user375123
    Commented Aug 16, 2023 at 13:26
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    $\begingroup$ @ASCD - Your question is not a mistake. It's a very good question! However, at the moment the question does not have an answer. Researchers continue to work on it! $\endgroup$
    – Prahar
    Commented Aug 16, 2023 at 16:44

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The information paradox is the tension between the following statements:

  1. The evolution of any quantum state is given by a unitary operator. This means that the evolution of any state should be deterministic, i.e., it should be possible to trace back the original state from the final state.

  2. General relativity is obviously deterministic too.

  3. When we combine General relativity and quantum mechanics we obtain that given an initial quantum state, if it forms a black hole, it will radiate thermal radiation until it fully evaporates. The end state will be a gas of uncorrelated radiation that doesn't hold any information about how the black hole was formed.

There are several philosophies proposed. Here are a few:

  1. Maybe we should give up unitary evolution (i.e. determinism) in quantum mechanics and replaced it by a more fundamental theory. This is not very popular since quantum mechanics has been wildly successful so any modification needs to still make every correct prediction in the last century.

  2. Once the black hole evaporates, there's a remnant holding all the information. This is also not very popular because an object like that would have an arbitrarily high entropy but be otherwise small, which we haven't observed at all.

  3. The information is stored in soft particles at the horizon. Soft particles are massless particles whose energy is infinitesimally close to zero. Because they basically don't exist (almost), most calculations tend to naively forget about them. Careful analysis shows that they do exist and have physical effects. Although soft particles are a candidate for where to store the "lost" information, the mechanism for this to work is far from resolved.

  4. Quantum gravity effects. Recently, research has shown that if we treat gravity quantum mechanically and sum over possible quantum states of spacetime, we end up getting strange non-local effects that correct Hawking's initial calculation and allow for correlations between the radiation and the black hole's interior.

In order to say that the paradox is resolved, the scientific community needs to agree on the solution. For example, we can say that the ether problem or the UV catastrophe are fully resolved because the scientific community agrees that the first is solved with special relativity and the latter with quantum mechanics. Every university teaches these topics. This is NOT the case with the information paradox, which is still an open area of research.

A satisfactory resolution should be able to describe the black hole quantum mechanically and reproduce the Page curve. This is the plot that tells you how the entropy of the black hole evolves with time and how the information leaks into whatever final state holds the information about the initial state.

I should also mention that I might be forgetting a few possibilities! I just mentioned the ones I am a bit more familiar with.

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Information Paradox is not resolved, no theory can totally resolve it, still breaking conservation of Information, still research.

But some theory can explain it but not much also not widely accepted: This theory is much accepted, explaining the paradox:

Quantum Hair Theorem:
https://arxiv.org/abs/2112.05171
As matter collapses into a black hole, they suggest, it leaves a faint imprint in its gravitational field. This imprint is referred to as “quantum hair” and, would provide the mechanism by which information is preserved during the collapse of a black hole.

The 'quantum hair' allows information from behind the horizon to emerge in Hawking radiation, so that an evaporating black hole obeys a property called quantum unitarity (Unitarity, as the principle is called, says that something always happens).

These resources can help you:

  1. https://www.sciencedirect.com/science/article/pii/S0370269322001290#:~:text=Abstract,the%20initial%20black%20hole%20state.
  2. https://www.livescience.com/stephen-hawkings-famous-black-hole-paradox-may-finally-have-a-solution#:~:text=One%20of%20physicist%20Stephen%20Hawking's,created%20them%2C%20new%20research%20indicates.

I hope now you can understand.

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