Hawking Radiation: Understanding Complexity in Black Holes

[hideelo]

If we take the perspective that black holes thermalize (reach maximum entropy) in a very short time and then just sit there and grow in complexity, how do we interpret Hawking radiation in this picture? i.e. you can't just have the state of the black hole keep growing in complexity forever, since at some point the black hole radiates away, so can the statement that the black hole evaporates be framed in a language of something happening to the complexity of the state of the black hole?

 

[PeterDonis]

If we take the perspective that black holes thermalize (reach maximum entropy) in a very short time and then just sit there and grow in complexity

Where are you getting this perspective from? If the hole has reached maximum entropy, how can it "grow in complexity" thereafter?

 

[hideelo]

Where are you getting this perspective from? If the hole has reached maximum entropy, how can it "grow in complexity" thereafter?

This takes it's origin by ideas promoted by Susskind Maldacena, Swingle, and many others

https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.116.191301

 

[hideelo]

Where are you getting this perspective from? If the hole has reached maximum entropy, how can it "grow in complexity" thereafter?

To directly answer your question, the idea is that while it reaches a maximal entropy state in a very short time, the space of maximal entropy states is not uniform. They give a measure on the space of states that is defined by how many "simple operations" are needed to get from the initial state to the state in question. The more such operations needed, the more "complex" the state

 

[PeterDonis]

This takes it's origin by ideas promoted by Susskind Maldacena, Swingle, and many others

The article you linked to is behind a paywall and I can't even read the abstract. Is there a paper on arxiv? Or at least can you give cites to papers, so I can try to look them up?

 

[PeterDonis]

the space of maximal entropy states is not uniform. They give a measure on the space of states that is defined by how many "simple operations" are needed to get from the initial state to the state in question.

On its face this doesn't make sense, since if two states require a different number of "simple operations" to be reached from some fixed initial state, they should have different entropies.

I suspect this is going to be one of those cases where there is no experimental evidence to bring to bear, and it comes down to different physicists' opinions about what kinds of theoretical operations "make sense" or something similarly vague. But for sure, we need to base discussion on something more specific from whatever references you have than what you have given so far. This is an "A" level thread, so you should be able to give the mathematical details that are claimed to justify whatever you are asking about.

 

[PAllen]

this link gets around the paywall issue:

https://link.aps.org/accepted/10.1103/PhysRevLett.116.191301

 

[PeterDonis]

this link gets around the paywall issue

Thanks, this is helpful!

On a quick read, by "black hole" they mean "black hole in Schwarzschild-AdS spacetime", which is not the spacetime we actually live in. So as I suspected, this is one of those cases where there is no experimental evidence and it's a matter of the theorist's opinion whether anything about such "black holes" is relevant to our actual universe. (I lean towards "no", but that's just as much a personal opinion as anyone else's--we have no way of testing the claim either way.)