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in popular science, the concept that information is lost beyond the black hole's event horizon is put forward.

But we know that black holes also have a mass, which is a type of information, and they can grow through an accretion disc. Let's assume that a black hole swallow a proton: then the mass of the black hole has increased 10^-27 kg (that is considering negligible any energy dissipation in the process of swallowing mass). In other words the information regarding the mass of the proton is not lost but transferred to the black hole.

So is the concept of loss of information within a black hole a myth? Is the reality more complex?

And if mass can be maintained, are there other physical characteristics that are kept within a black hole? For instance, the Hawking radiation implies that black holes have a temperature, that is thermodynamic information. And they radiate X-ray thus they have an electromagnetic information.

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  • $\begingroup$ "So is the concept of loss of information within a black hole a myth?" The information loss paradox arises when we try to combine quantum physics and general relativity in a naive way, and the paradox has survived decades of very careful analysis. The modern consensus is that information is not lost but that evading the naive paradox requires a proper theory of quantum gravity, and we don't have a detailed understanding of this yet. For more about this, with references, see Why is the information paradox restricted to black holes? $\endgroup$ – Chiral Anomaly Aug 6 '19 at 13:34
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According to the No-hair conjecture, a stable black hole can be completely described by its mass-energy, electric charge, angular momentum, linear momentum, and position. The last two can be canceled out by a choice of coordinates, so famously, a black hole "remembers" only its mass, charge, and angular momentum.

In the example of a proton, the information of its mass-energy, electric charge, and spin (intrinsic angular momentum) would remain (along with the linear momentum) by adding to the totals. However, the information of the baryonic number or anything else would be lost (or at least unobservable from outside).

In this sense, black holes made of matter or antimatter (or half and half) are indistinguishable, as well as hypothetical black holes made of light, dark matter, neutrinos, or anything else of a sufficient energy. All we can measure is the total mass, charge, and angular momentum.

The temperature of the Hawking radiation is defined by the total mass while its mostly electromagnetic spectrum of a black body is defined by random processes with no additional information.

This conjecture is known also as a No-hair theorem, as it has been proven for the most common uncharged, charged, non-spinning, and spinning black holes. However the rigorous proof of a general theorem remains an open problem in mathematics.

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Suppose you drop a molecule of your DNA into the black hole. There is far more information in the molecule of DNA than just its mass. Indeed, there is enough information to make you. But the only information we have about the black hole is its mass, spin and charge, so once the molecule is inside the black hole the huge amount of information stored in it is inaccessible.

Note that the information loss problem isn't the fact that information behind the event horizon is inaccessible. The information hasn't been lost even though we no longer have access to it. The problem is that black holes evaporate due to Hawking radiation and the radiation emitted during the evaporation doesn't contain the same information as the held in the matter (DNA in this example) that fell in. That means once evaporation is complete the black hole has gone and the information concealed within it has gone too.

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  • $\begingroup$ But many simple processes can destroy information like the DNA. For example, if you just burn a DNA molecule, the information is lost forever. If a piece of paper has information written on it, and you destroy the paper, the information is lost. This is trivial. Then why is a similar information loss in Black Holes is a big deal to the point it's continually discussed? $\endgroup$ – Ryder Rude Aug 6 '19 at 7:36
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    $\begingroup$ @RyderRude When you burn DNA the molecules like CO2 and water produced have well defined velocities. In principle, though not in practice, you could measure the positions and velocities of all the molecules produced by burning the DNA and then trace these back to reconstruct the original DNA molecule. So the information is not lost, only converted into a different form. By contrast, if you drop the DNA into a black hole, then the black hole evaporates, the information is truly lost i.e. there is no way to reconstruct the DNA by observing the particles produced during the evaporation. $\endgroup$ – John Rennie Aug 6 '19 at 7:41
  • $\begingroup$ But Quantum world is probabilistic and uncertain. In a Newtonian world, we could trace back every particle because things are predictable. But there is uncertainty in QM. $\endgroup$ – Ryder Rude Aug 6 '19 at 8:38
  • $\begingroup$ @RyderRude yes, and that means we could never reconstruct the DNA molecule exactly. But this is no different to saying we could never exactly measure the position of the DNA molecule and the oxygen molecules it reacts with before the combustion i.e. the uncertainty of the measurements before and after the combustion is the same. With the black hole evaporation all the information is irretrievably lost. $\endgroup$ – John Rennie Aug 6 '19 at 8:42
  • $\begingroup$ What does a Black Hole do to the thing it swallows that normal physical processes like burning or tearing things apart don't do? $\endgroup$ – Ryder Rude Aug 6 '19 at 8:46

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