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It is usually said that according to the no hair theorem, black holes erase the information enter them which reduce the entropy and imply the so called "information paradox".

The problem is that for an observable far from the black hole, you can't really throw anything inside it because the time take for an object to get to the horizon would seem infinite so it seems to me that no information can be lost in that way.

Is it right and if so, how it fit together with the information paradox?

ziv
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  • You might be interested in this Q/A: https://physics.stackexchange.com/a/739114/27732 – Andrew Feb 07 '23 at 00:58
  • @safesphere so the only "problem" is with the rising of information after evaporation? – ziv Feb 07 '23 at 05:25
  • I understand, but if black holes have only one states, and radiation is random (so it has some entropy), I don't see how you avoid the rising of entropy from 0 to some value that fit the radiation – ziv Feb 08 '23 at 08:19
  • @safesphere sure , I also wrote in my comment that entropy increase , not information. – ziv Feb 08 '23 at 22:18
  • @safesphere sure , I also wrote in my comment that entropy increase , not information. As I understand it now, the entropy decreases and also information is lost when the black hole formed. Then only entropy increase while information stay the same during evaporation. Also I thought about it more carefully and I think that we have to consider the new radius of the black hole that rise due to the mass we throw inside it. The mass will not cross the previous horizon but it will cross any larger radius hence from our perspective the mass will get eaten by the black hole – ziv Feb 08 '23 at 22:25
  • @safesphere If you agree with that I will add my solution as a answer for this question – ziv Feb 08 '23 at 22:25
  • Sure, I meant that the entropy as originally defined decrease and this also motivate us to define entropy associated the the BH area so does the total new entropy obey the regular second law of thermodynamics – ziv Feb 09 '23 at 12:21

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