The Hawking temperature equation states that the temperature of a black hole is inversely proportional to it's mass, and and the black hole loses mass when it emits particles in the form of radiation, which is thought to erase information according to the black hole information paradox. So, is it possible for this information or energy to be present in the another form for example thermal energy when a black hole loses mass as temperature increases?
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1$\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$– Community BotCommented Jun 23 at 9:02
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1$\begingroup$ Do you happen to have some idea what form of energy a black hole has, before any conversion of energy? $\endgroup$– stuffuCommented Jun 26 at 9:08
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$\begingroup$ Why would Hawking radiation decay? $\endgroup$– PM 2RingCommented Jun 26 at 9:53
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2 Answers
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The reason that information is lost according to the information loss paradox is that Hawking radiation is completely thermal radiation, meaning that it is uncorrelated and carries no information other than the mass and temperature of the black hole. However, just from the mass and temperature of the black hole it is impossible to reconstruct what fell into the black hole, which implies that information is lost in the evaporation process.
A more technical description is that if the black hole evaporates completely, then an initially pure state will have evolved into a mixed state. Therefore, information must have been lost unless the correlations between the inside and the outside of the black hole are somehow restored during the evaporation process.
Lastly, it is important to note that the formulation of the information loss paradox rests on the assumption that the black hole has an event horizon (which takes an infinite amount of time to form according to distant observers). On the other hand, for a black hole bounded by an apparent horizon (or some related quasilocal notion like a trapping horizon) information can escape eventually and there is no paradox. See also the discussion here: https://doi.org/10.1103/PhysRevD.105.124032
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$\begingroup$ "the correlations between the inside and the outside of the black hole" - This is a popular misconception among physicists. The inside is in the future relative to the outside and therefore cannot have any effect on the outside. This means, if the mass of the collapsed star gets inside, it disappears from the outside world while violating energy conservation. Fortunately this is not the case and all mass of the collapsed star ("black hole") remains outside the horizon until the black hole evaporates. $\endgroup$ Commented Jun 23 at 10:13
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$\begingroup$ "information can escape eventually and there is no paradox" - This also is not true. The paradox is deeper than its vague quantum interpretation. If I am in a free fall, then by my (or anyone's) clock the black hole evaporates before I reach the horizon. Therefore I expect to remain intact (neglecting the tidal and other destructive forces), but all my mass/energy has evaporated, so I must disappear. The paradox is not limited to the quantum states, but is there at the classical level as well. The root of the paradox is that a black hole is the effect of things located outside the horizon. $\endgroup$ Commented Jun 23 at 10:24
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3$\begingroup$ You might want to read up on some proper literature before spreading misinformation as there is already a lot of confusion on the topic of black holes and in particular on the information loss problem. Chapter 6 of Wald's review should be a good start: doi.org/10.12942/lrr-2001-6 The fact that black holes bounded by quasilocal horizons have a quantum ergosphere, i.e. a region from which information can escape, is also well known, see, for instance, the original paper by York: doi.org/10.1103/PhysRevD.28.2929 $\endgroup$ Commented Jun 23 at 10:33
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$\begingroup$ There is nothing logical about your argumentation. You are simply claiming that everyone is wrong and you are right without having anything to back it up with. As for your "arguments": If you had taken the time to actually engage with the literature on black holes rather than dismissing it you would see pretty quickly why what you are writing does not even make sense. Best of luck. $\endgroup$ Commented Jun 23 at 23:16
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1$\begingroup$ The fact that you have deleted your nonsensical comments rather than owning up to them is telling. $\endgroup$ Commented Jun 24 at 9:08
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If a large amount of non-rotating thermal energy collapses into itself, the result is a non-rotating black hole, whose energy is thermal energy.
If one unit of thermal energy is conducted away from aforementioned black hole, then it has one unit less thermal energy.
In other words, if aforementioned black hole emits one Joule of Hawking radiation, which is thermal energy, then it has one Joule less thermal energy.
The above is an answer to the energy part of the question. Now the information part is left.
Hmm well, when black hole has evaporated, there is nothing left of the black hole, except the Hawking radiation. So the information that was in the black hole is either in the Hawking radiation, or it has disappeared.
Which alternative is true, is not known.
