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$\underline{Background:}$

Two characters, Alice(overused name for contexts like these) and Jake are in space next to a black hole(BH). Now if Jake's position is fixed in space and Alice gets sucked by the BH, in Jake's frame of reference, one would see Alice moving towards the BH forever. The closer Alice get's to the BH's horizon, the slower she would appear to move. After some time, when Alice reaches the horizon, Jake sees her freeze. Alice remains plastered there, motionless, stretched across the surface of the horizon as the heat begins to engulf her. With respect to Alice's frame of reference, she is long dead. Time ticks slowly around a BH, as it 'bends' space-time.

$\underline{Physical setup:}$

Let Jake's frame of reference be 'α' and Alice's frame of reference be 'Ω'. From α, initially information about Alice was well defined and it kept changing as Alice traverses in space, but after Alice reached the event horizon of the BH, the information ceased with no updates. From Ω, however, information about α is well defined initially and changes as Alice traverses in space, but all of a sudden the information vanishes when Alice reaches the event horizon. Now for the Alice(an imaginary Alice who does not exists but survives with her frame of reference inside the BH being ε) inside the BH, the information of herself in Ω,outside the BH,is unknown. Also she cannot transmit information of her existence from ε to Ω or α due to time dialation.

A crude picture of the setup:

enter image description here

Now my questions:

1. With the above being said; before the Alice plummets into the BH, before she moves towards the BH and before she separates from Jake. Would Alice inside the BH(her future self) at ε be able to obtain Alice's and Jake's information from Ω and α, respectively?

I have asked this question because once Alice moves towards the BH, her information is well defined and certain(more crudely put, her fate is almost certain), so the information of Ω is already well defined at ε before the event even occurs. And since information of Ω is known, the information at α also becomes well defined(but can future Alice distinguish the difference in information between that of Ω and α?). However, one cannot access the information of ε at Ω due to the slowing of time around a BH(as the time taken for information to relay back would get delayed continuously).

2. If information about the inner side of the BH is unknown to the outside space(as it cannot be relayed), doesn't it mean that the universe is unaware of the BH's existance? If this is so then the information about the lifetime of the BH goes undefined,thus immortalising the BH(from the universe's frame of reference)

Part A: If Hawking's theory is true then the life of the BH is well defined at ε, and it would eventually die, but never at Ω, hence according to the universe the information of space being occupied by a BH becomes unknown and BH's don't exist from the universe's frame of reference.

Part B: If the universe is aware of the BH's existence and its lifetime(let's define a time space:"Now"), then doesn't it mean that information has travelled(from ε to the universe) faster than the speed of light providing information about the BH's future?

Please note: I spent a lot of time thinking about the following, and even more time thinking whether to post this on SE or not. I might make sense to you or might come across as 'terribly confused'. Any reflection would be much appreciated.

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  • $\begingroup$ Do your symbols represent spactime events, or inertial reference frames? $\endgroup$ – benjimin Oct 25 '16 at 20:42
  • $\begingroup$ @benjimin α-frame of reference of Jake, Ω-frame of reference of Alice(moving towards BH) and ε-frame of reference of Alice(imaginary, inside BH). $\endgroup$ – Naveen Balaji Oct 25 '16 at 20:45
  • $\begingroup$ A frame of reference as in a coordinate system for an arbitrarily large neighbourhood? Then what do you mean by something travelling toward it? $\endgroup$ – benjimin Oct 25 '16 at 23:19
  • $\begingroup$ @benjimin by saying so I just meant :'from their perspective ' $\endgroup$ – Naveen Balaji Oct 26 '16 at 14:10
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    $\begingroup$ What do you mean by information of the lifetime and existence of the black hole? (Also, by time space do you mean Cauchy surface?) $\endgroup$ – benjimin Oct 26 '16 at 20:27
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No, the universe is unaware of the existence of the BH, nor of any of the space inside the horizon -- actually all the spacetime the BH occupies is disconnected casually from the rest of the universe. A perpetual BH always existed and always will, and the spacetime it occupies (and all 'within' the horizon) is just not part of our universe.

A real (non perpetual) BH is almost the same, we actually can't note a difference, except it is in an infinite process (from our point of view, due to time dilation) of forming. For all 'practical' purposes they are the same. We just cannot see the spacetime inside.

The first part, as Benjimin said clearly, Alice's time is very limited. The falls towards the horizon, goes through it, and she then falls into the singularity in a very short period of time.

The two merging black holes first ever detected merging in 2015 had their final merger phase happening in 1/4 second. The final part of the gravitational wave detected was their merger. It shows how fast it happens, for two massive bodies, each more massive than 20 solar masses, falling into each other.

See about two black hole mergers, and information on the first discovery at https://en.m.wikipedia.org/wiki/First_observation_of_gravitational_waves

See the simulation at https://m.youtube.com/watch?v=I_88S8DWbcU

Alice has no chance.

As for information loss, as of now there is still no solution. Hawking's finding that BHs evaporate by emitting radiation which tunnel out of the BH through a quantum process (so it is a quantum effect, pure general relativity without a quantum field to treat would have no mass evaporating). Also, his calculations showed that the radiation coming out was random, un correlated with anything, so it was not the information that went in. But it was a pseudo-quantum treatment, the field was quantum but gravity was classic. Not a full quantum gravity treatment. People have been trying to figure it out, no real success yet. Hawking published a paper with 2 colleagues early in 2016 Where he found that there are, other conserved quantities in horizons, he called them 'soft hair', that they claimed may be, after a full quantum treatment (which they only did partially, and admitted it, so they couldn't show what they wanted to), may be where the information going into the black holes is actually stored.

See his arxiv paper at https://arxiv.org/abs/1601.00921

Professional publication at http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.231301

It's not been proven, and other people have tried to find ways in which what comes out of the black holes, during evaporation, carries correlated information from the mass falling in. Another approach has been to try to use the AdS/CFT correspondence to show that the information is in the horizon. So far there's been no real resolution.

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  • $\begingroup$ Thanks a lot! Just one clarification , there is only one BH here and no merging takes place, and also who do you refer to as Shen? $\endgroup$ – Naveen Balaji Oct 26 '16 at 3:20
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    $\begingroup$ Sorry Naveen. Shen meant 'she', the word checker in my iPad is crazy. As for the two black holes, sorry for the confusion also, I edited it to say how that fits in. It is a different story than Alice and Bob (or whatever his name), I just put it in for people to realize we had already detected a balc hole getting formed, from two smaller ones. You are right, Alice just falls into 1. Just that it happens quickly. $\endgroup$ – Bob Bee Oct 26 '16 at 5:38
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  1. Yes. Alice's minutes are numbered. She will cross the event horizon within a finite amount of her time, although it will be very difficult for her to discern exactly the instant that she crosses. After she crosses, she will have only finite moments before the singularity. But during those short moments, she will still be able to look outside and see Jake (and potentially receive any messages Jake sends).

  2. No. (And the question seems to involve some false premises due to confused concepts or sloppy terminology.) Lacking precise foreknowledge of your future is not immortality.

If there was no Hawking radiation, the black hole would never evaporate.

If the black hole does evaporate, it suggests that information that went to the event horizon has come back (in scrambled form) from the horizon again. It is probably safest to assume this information comes from no deeper than the horizon and thus didn't exceed the speed of light (and can't relay messages from the interior, except in so far as by the holographic principle you can predict what would have happened in the interior if you somehow unscramble perfect information about what went in). But you are starting to approach questions that will be unanswered until physicists learn more about quantum gravity.

Edit It sounds like you are imagining the black hole might grow or shrink in an uncoordinated way that causes the size of the interior region to mismatch what it seems to occupy from the exterior universe, like a TARDIS. It might help to look at Penrose diagrams. The interior region (that Alice crosses into) is entirely in the future of the exterior region (and the exterior is in the past of the interior region)..

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  • $\begingroup$ Thanks for the answer!By the immortalising(was just used as a figure of speech to convey the message informally, agreed that it is not the best word to use) all I meant was that since the universe is unaware of the BH's existance, spatially the BH continues to exist forever, occupying space. However we don't know if this is true, hence the part A of my question, addressing Hawking's theory that shines light upon the information retrieval from a BH. $\endgroup$ – Naveen Balaji Oct 25 '16 at 20:54

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