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Consider the Penrose Diagram of Collapsing Gravitational matter :

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Any radial light ray (say P) originating from $\mathscr{I}^{-}$ is bound to end up in the Black Hole. The causal past of $i^{+}$ implies that anything in that region can (and not must) influence it. But even though P lies in the causal past of $i^{+}$ it cannot influence $i^{+}$ since it fell into the Black Hole.

  1. Why is that so?

  2. Is this analogous to the BH Information Paradox? I thought that the paradox was only there when considering quantum effects i.e. evaporation of Black Hole.

Edit - A little clarification

The paradox is only one part of the question. The main thing is to understand that why things which can, in principle, causally affect others things are unable to do so.

(How do I connect it with the Information Paradox? :) Does this not mean that some kind of information is not able to reach regions which it should? It is getting lost in the BH and in that way it appears a bit like the Information Paradox. That's why the question is framed as another form of Black Hole Information Paradox.

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  • $\begingroup$ This is the penrose diagram of a classical black hole created by gravitational collapse. It does not tell us anything about the information paradox, which as you have right mentioned, occurs due to quantum effects. $\endgroup$
    – Prahar
    Commented Sep 17, 2020 at 21:27
  • $\begingroup$ @Prahar Please see the edit. I tried to clarify what I meant. $\endgroup$
    – self.grassmanian
    Commented Sep 18, 2020 at 7:04
  • $\begingroup$ @ChiralAnomaly I agree but I just happened to notice this while studying the above and made the connection with the paradox. $\endgroup$
    – self.grassmanian
    Commented Sep 18, 2020 at 7:05
  • $\begingroup$ @Prahar Also, upon further thought I would say that the paradox does not arise from quantum effects but rather when you consider the quantum theory + apply the unitarity. No effect is necessary to produce the paradox, right? Just a consequence of a principle of quantum nature. $\endgroup$
    – self.grassmanian
    Commented Sep 18, 2020 at 7:36
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    $\begingroup$ The information paradox occurs only after the black hole has evaporated. No evaporation, no paradox. Classical black holes never ever evaporate, so there is no information paradox whatsoever at the classical level. The paradox arises quantum mechanically when essentially two different quantum effects seemingly contradict each other. $\endgroup$
    – Prahar
    Commented Sep 18, 2020 at 11:27

2 Answers 2

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enter image description here

I whipped up a quick picture. Excuse my drawing, I’m in a moving vehicle right now.

Some geodesics enter the black hole as you have shown, and some others escape out to infinity.

A comment about the definition of causal past. Every point in the causal past of a point P CAN affect P, but does not have to - meaning that there exists a geodesics that connects P and every point Q in its causal past, but not all geodesic through Q reaches P.

There is no paradox. None of this is related to the information paradox.

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  • $\begingroup$ And is it okay if things in causal past are not able to effect an event necessarily (the first question basically)? I understand that there is no information loss paradox in the conventional sense but what I meant is that if some information from the past is not able to reach a future point then this must be a paradoxical situation and hence the terminology. Don't be concerned about the terminology used. $\endgroup$
    – self.grassmanian
    Commented Sep 18, 2020 at 11:44
  • $\begingroup$ Alternatively, I could say it like this : Not all the information from causal past of an event is available to it. Is such a scenario okay? Don't we have any problems with this? $\endgroup$
    – self.grassmanian
    Commented Sep 18, 2020 at 11:46
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    $\begingroup$ I’ve edited my answer a bit. I think it answers your question. A surface which has access to ALL the information in its causal past is known as a Cauchy surface. In the presence of a black hole neither time like or null infinity are Cauchy surfaces. $\endgroup$
    – Prahar
    Commented Sep 18, 2020 at 11:58
  • $\begingroup$ That does it. I was under the impression that all surfaces have to be, as you pointed, Cauchy surfaces. Thanks! $\endgroup$
    – self.grassmanian
    Commented Sep 18, 2020 at 12:07
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    $\begingroup$ Even when there are no singularities, $i^+$ is not a Cauchy surface. In good old Minkowski space time, $i^+ \cup {\mathscr I}^+$ is a Cauchy surface. $\endgroup$
    – Prahar
    Commented Sep 18, 2020 at 12:20
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It's not true that any light ray from $\mathscr{I}^{-}$ must end up in the black hole. A generic ray won't get anywhere near the hole; it'll be slightly deflected and head off to future null infinity. Only purely radial rays follow 45° lines in the Penrose diagram.

Even radial rays won't necessarily end up in the hole. There could be a mirror in the way. Or there could be a mirror oriented sideways that doesn't deflect the light enough that it misses the hole, but still picks up some momentum from it, which can be seen from $i^{+}$. And so on.

I don't think this is related to the black hole information paradox.

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    $\begingroup$ This essentially addresses only one word (and one misconception on part of OP) of the question: “any”. The conclusion that this in unrelated to BH information does not follow from the argument. $\endgroup$
    – A.V.S.
    Commented Sep 18, 2020 at 3:50
  • $\begingroup$ @A.V.S. I thought I completely answered the question, but it's possible that I didn't understand the question (in which case I still don't). $\endgroup$
    – benrg
    Commented Sep 18, 2020 at 5:14
  • $\begingroup$ @A.V.S. Agreed. Please see the edits I made in the post to try to make things clearer. Besides, I meant radial rays only but forgot to mention it, which has been corrected. What A.V.S. meant is that I was asking for any (radial) ray and your answer just addresses some of the radial rays. $\endgroup$
    – self.grassmanian
    Commented Sep 18, 2020 at 7:09

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