Event Horizons in General Relativity

Discussion in 'Astronomy, Exobiology, & Cosmology' started by RJBeery, Apr 17, 2019.

  1. RJBeery Natural Philosopher Valued Senior Member

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    Summary
    In this post we will examine the logical conclusions to be drawn in a world described by General Relativity (GR) which also shares certain common observations made in our own world; the chief of which is that event horizons, as described by GR, are not compatible in such a world.

    Event Horizons
    The prediction of black holes and/or event horizons in GR is generally not up for debate. The mathematics are well understood, and, in the world examined in this paper, we would indeed expect black holes “to exist”* when the appropriate conditions have been met.

    Now consider the following. During the construction of the Large Hadron Collider a study was done, partly to assuage laymen’s fears, regarding the safety of colliding elementary particles at extreme velocities. A common concern expressed by the public was that a black hole might be produced and destroy the planet. The LHC Safety Assessment Group’s response [1] was

    In the case of the hypothetical microscopic black holes, as we discuss in Section 4, if they can be produced in the collisions of elementary particles, they must also be able to decay back into them. Theoretically, it is expected that microscopic black holes would indeed decay via Hawking radiation, which is based on basic physical principles on which there is general consensus. If, nevertheless, some hypothetical microscopic black holes should be stable, we review arguments showing that they would be unable to accrete matter in a manner dangerous for the Earth [2]. If some microscopic black holes were produced by the LHC, they would also have been produced by cosmic rays and have stopped in the Earth or some other astronomical body, and the stability of these astronomical bodies means that they cannot be dangerous.​

    It is clear that there is a “general consensus” on the “basic physical principles” which would accept that the appropriate conditions for black hole creation from cosmic rays exist. There is also, presumably, a consensus that such black holes are not appearing in our labs, despite the appropriate conditions for their formation.

    This is a crucial point. GR is unequivocal about the fact that event horizons cannot exist in an observer’s past light-cone. The absence of microscopic black holes in our labs extends into our historical record, and our labs of yesterday are clearly within our past light-cones. If we demand that GR is correct, then we are forced to conclude that our “black holes” were never formed in the first place and that a dissipative process has apparently occurred. It should also be noted that this dissipative process cannot be Hawking Radiation, because such radiation relies on the existence of the event horizon to occur. Indeed, Hawking Radiation is left dangling as a logical contradiction in a world whose black hole formation exists solely in the future.

    Conclusion
    In this paper we have presented a logical contradiction when we try to reconcile the formation of event horizons as predicted by GR with the observations made in our labs; we have concluded that an as-yet-undescribed dissipative process must exist which affects the conditions for black hole formation, occurring prior to such formation, if we are to apply General Relativity to our own world.

    * For purposes of this paper we are using the most lenient definition of what it means “to exist” without semantic or philosophical considerations.

    References

    [1] LHC Safety Assessment Group, Review of the Safety of LHC Collisions. http://lsag.web.cern.ch/lsag/LSAG-Report.pdf
     
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  3. NotEinstein Valued Senior Member

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    I've never heard of that; can you please point me to some sources?

    What paper?
     
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  5. RJBeery Natural Philosopher Valued Senior Member

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  7. NotEinstein Valued Senior Member

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    Then I'm going to request one of those, because it's not clear from that page and the picture you posted that's the case. In fact, I think it demonstrates it to be incorrect. Look at the light-cones at the top of the picture, and draw their full past light-cone. Are you saying they will never intersect with the event horizon, not even if one start drawing the light-cones of observers close to the event horizon but far in the future?

    Also, I've got a picture too: https://www.nasa.gov/mission_pages/chandra/news/black-hole-image-makes-history/
    It's the famous black hole picture, showing an event horizon. Please explain to me how that isn't an event horizon currently in our past light-cone?

    I'm not saying you're wrong, but I've simply never heard of the claim and at first glance (including with what you just posted) it seems to be incorrect.
     
  8. NotEinstein Valued Senior Member

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    Actually, I think I figured it out on my own. The light-cone can be taken to be "malleable"; it will "wrap around" the event horizon, never including it. Just draw photon trajectories, and realize they are the light-like separation between the "elsewhere" and the "past" sections of the light-cone. In some sense, the black hole "punches" a hole in the past light-cone to exclude itself from it. So let me get back to the OP with this new insight.

    The labs, yes, but not any black holes contained within. The black hole would bend the past light-cone around itself, and would never be included in it, even though the lab surrounding it would be.

    (And no, I also cannot properly visualize this 3+1D situation.

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    )

    A good way to reason about this is with the photon trajectories I already mentioned. We can and have observe(d) the lab, so clearly it is in our past light-cone. We cannot observe the event horizon itself directly, or anything on the inside of it, so it's not in our past light-cone. It clearly isn't in our future light-cone either, (and it's not light-like) so it must be in the "elsewhere"-section.

    This is thus a bad conclusion; black holes can form just fine, but they will always be in our "elsewhere" (or "future") sections of the light-cone. They will punch a hole in the past light-cone if needed.

    It actually makes sense: there is no causal connection between anything inside the event horizon and outside of it; exactly like the "elsewhere"-section.

    (This is then also unwarranted.)

    You are forgetting the possibility of black holes in the "elsewhere"-section. In fact, don't you *have* to include that, because if a black hole forms in our future, it will be forming in the "elsewhere"-section of some other observers?
     
  9. RJBeery Natural Philosopher Valued Senior Member

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    But I'm restricting conversation to General Relativity which claims that events relative to an observer are either time-like, space-like, nor light-like; the idea that there is a mysterious noncontinuous "elsewhere section" is plausible but it isn't General Relativity. If you extend the past light-cones backward in the picture I referenced you'll see that the event horizon lies in none of them but remains space-like separated from all observers.

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  10. NotEinstein Valued Senior Member

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    So am I. Nowhere have I introduced anything else.

    Correct, and nowhere have I introduced anything else.

    See, that's where you can't have your cake and eat it too. Either the light-cone is not malleable and black holes can be located in the past light-cone, or not.

    At first, I thought that too. But it's an anomaly of the picture, because the light-cones aren't drawn into the future far enough for it to happen, as I stated:
    Take that light-cone top center-left where you've drawn that red line. Draw the light-cone of an observer that's "one inch" (or perhaps two; whatever is needed) further into the future. The angle of the red line will be exactly the same (assuming, just like the picture, that the black hole isn't growing). How can its red line not intersect the event horizon?

    You have chosen the light-cone to be non-malleable by drawing the red line straight, even though spacetime is curving. Look at the right-most red line when it hits the closest-to-the-event-horizon light-cone: the red line doesn't match with that light-cone's light-like angle. This means that the light-cones are only "correct" (as in: they keep their meaning) locally. Basically, you are using "SR light-cones". As I just demonstrated, this way the black hole will end up in your past light-cone. Also, you'll have photon-trajectories that, at distance, don't fall in the light-like part of the light-cone. All of which is perfectly fine, as long as you realize that this choice of light-cone treatment only allows you to locally draw conclusions.
     
  11. RJBeery Natural Philosopher Valued Senior Member

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    Because if the observer were "one inch" further into the future his light cone would be situated at a different angle...just like all of the other observers in the picture; the higher they are, the more their light cones are tilted such that their past light cone does not contain the event horizon. With respect, I'm not interested in convincing you of a well-established feature of General Relativity.
     
  12. origin In a democracy you deserve the leaders you elect. Valued Senior Member

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    You seriously came to that conclusion based on these statements?
    How you came to the conclusion that cosmic rays can create black holes is beyond me.
     
  13. RJBeery Natural Philosopher Valued Senior Member

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    Black holes themselves are a hypothetical consequence of General Relativity. Hypothetical literally means "as predicted by a theory" and in this case the theory is General Relativity. Predicting black holes from cosmic rays would be a function of their estimated energy. I can only read your comment to mean that you don't personally believe that cosmic rays can create micro black holes (which is fine) but also that you believe that astronomers in the physics community don't either (which is odd). Have you read section 4 of the LHC Safety Assessment?
     
  14. NotEinstein Valued Senior Member

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    So the curvature of spacetime caused by a static black hole decreases over time, to the point that eventually you'll have pretty much flat spacetime right next to the event horizon? Please provide sources for this "well-established feature of General Relativity", because I've never heard of it.
     
  15. RJBeery Natural Philosopher Valued Senior Member

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    Wald's definition of a black hole in asymptotically flat spacetime is that portion which is "not in the causal past of future null infinity." Are you familiar with Wald?

    https://www.mathpages.com/home/kmath339/kmath339.htm

    It should be obvious that anything in your past light cone is, by definition, is in the causal past of future null infinity and therefore cannot be a black hole...which is another way of saying that a black hole cannot be in your post light cone.

    I don't mind discussing topics (or even arguing) but I frankly don't like googling references for others. Researching this on your own should not be difficult, unless you're just trolling me.

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  16. NotEinstein Valued Senior Member

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    That's a valid position, sure. What isn't valid is you still trying to have your cake and eat it too. If you say the black hole can't be in the past light-cone, that's fine, but then you can't have "SR light-cones". The light-cone needs to be "malleable" in that case.

    Unless you're going with your "spacetime becomes flat over time around a black hole" solution, for which you have yet to provide a source.

    So when you said:
    You were what? Lying?

    Why should I have to research it on my own? You are the one making the claims, and you are the one saying they have many sources. And if it isn't that difficult, why don't you do it in the first place?

    If anybody is trolling anybody, it's you trolling me. You keep ignoring key portions of my posts. You keep saying it's "well-established" and that there are many sources, but you then consistently fail to show that and produce them.
     
  17. arfa brane call me arf Valued Senior Member

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    But exactly how unequivocal? There does seem to be some confusion about what "observing" an event horizon actually means; everyone does seem to be able to understand that an observer passes through one, without noticing anything.

    Then there's the example of us, as distant observers of an astronomical "event horizon", which is an image of the particles around a black hole, interacting with each other as they orbit the horizon. What does that make us? How does GR make us into observers, and of what, in this case?

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    Is the event horizon of this astronomical object, in our past lightcone, in other words? Particles inside this horizon cannot send any information "our" way, or anywhere else. They're causally disconnected once they fall through the horizon. What we can see in the image is outside the horizon.
     
    Last edited: Apr 18, 2019
  18. DaveC426913 Valued Senior Member

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    Actually, this rings true for me.

    I asked a question on physicsforums about the LHC forming BHs, and I got schooled that the LHC is nowhere neat as powerful as cosmic rays can be, by several orders of magnitude. The gist of the discussion was that - since cosmic rays aren't causing BHs all the time, the LHC can't.

    But the implication there is that the connection between cosmic rays and formation of BHs is not a completely silly conjecture.

    I can link you to the discussion if you'd like.
     
    Last edited: Apr 19, 2019
  19. Write4U Valued Senior Member

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  20. RJBeery Natural Philosopher Valued Senior Member

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    This position confuses me. I think we both agree that the trajectory of a photon around a black hole would not be "straight". Geodesics in GR are definitely not straight, but I don't see why that should or should not determine a black hole can exist in a past light cone.

    Think about this for a second -- what does it mean for an event to "exist in your past light cone"? It means that a photon would be capable of reaching you from that event. Are you contending that black holes can exist in past light cones? Because if that's our only bone of contention then I have to ask whether or not you've read the references I provided. Are you refuting Wald's definition??
     
  21. NotEinstein Valued Senior Member

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    Really depends on your definition of "straight", but if you mean it as "straight (red) lines in the picture I posted" then yes, obviously.

    See, this is where you need to be more careful, because that statement is incorrect if read as written. It's false by definition; see the first line of the lead of this article: https://en.wikipedia.org/wiki/Geodesics_in_general_relativity

    Neither do I? I have no idea where you got that from, so I'm as confused as you are by this position you are talking about.

    Right, so the straight red lines you drew in that picture have nothing to do with the past light-cone, even though that was explicitly what we were talking about. Why did you draw those misleading lines?

    If I take the light-cones as you drew them in that picture, then it appears you yourself are contending that. I have already explicitly stated my position on this matter twice.

    And I have to ask whether or not you are reading my posts... You keep skipping important sections, you keep forgetting the parts where I explain my position, and you continually ignore my pointing out where your reasoning fails.

    No, as I already said: it appears you are, with your straight line picture.
     
  22. RJBeery Natural Philosopher Valued Senior Member

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    Yes, forgive me. Please let me know, right now and explicitly, if you believe that black holes can exist in an observer's past light cone, even if you've already explained your position.
     
  23. NotEinstein Valued Senior Member

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    It depends on the type of light-cone you are using. If you are using (what I termed) SR light-cones (draw a local light-cone, and use a ruler in the Minkowski diagram to extend it), then yes, black holes can exist in an observer's past light-cone, as your picture demonstrates (if you add light-cones "one inch" into the future). If you are using (what I termed) malleable light-cones (where you use photon and particle trajectories (or rather, causal connection) to determine the extend of the past light-cone) then everything inside and at the event horizon cannot be in the past light-cone.
     

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