Black Hole Entropy

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Is entropy consistent from all reference frames? For an observer at the surface of a blackhole, a finite amount of time would pass, but the observer would observe an unbounded amount of time passing for the outside universe, hence from his/her reference frame, information, entropy of the outside universe increases without bound, second law of thermodynamics. From the outside observer's perspective, the infalling observer redshifts into nothing. But they must agree on the same information content: that is, entropy, due to the laws of physics being invariant. Thus, blackholes have maximum entropy. This entropy is encoded on the surface of the blackhole since the outside observer never sees the infalling observer pass the event horizon. Is this reasoning correct?
 
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PeterDonis
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For an observer at the surface of a blackhole
There is no such observer; it is impossible to remain static at the horizon of a black hole. All observers must fall inward; they can only be at the horizon for an instant.

the observer would observe an unbounded amount of time passing for the outside universe
This is not correct. An observer falling into a black hole only sees a finite amount of time pass in the outside universe before he hits the singularity.

Is this reasoning correct?
Obviously not, since it's based on mistaken premises. See above.

Regarding the question of whether the entropy of a black hole is an invariant, as far as I know that is indeed the mainstream view. However, we don't know the microphysical details of how that entropy is "stored" in microscopic degrees of freedom. We probably won't have a good understanding of that until we have a good theory of quantum gravity.
 

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