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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.

Gigiux
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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.

John Rennie
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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.

safesphere
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