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I Black holes and the relativity of simultaneity

  1. Dec 24, 2015 #1
    Over the years I've watched Science try to deal with the Information Paradox regarding black holes.


    I've always been curious how we got to the point where we see this as a problem in need of a solution. In order for information to be "in" a black hole, and theoretically unavailable to us, it must have crossed the event horizon from our perspective, correct?

    We talk about the existence of black holes as a matter of fact, in present tense, but present tense existence of spatially distant objects (i.e. events) are space-like separated by any definition, and I don't think anyone will disagree with this. The temporal order of space-like separated events is ambiguous, and can be changed based on the frame of the observer. Now, follow this logic:

    Let's denote an event a "growth event" when matter crosses an event horizon. In order for a black hole to presently exist with a non-zero radius for an observer, that observer must have "growth events" in his or her past light cone. The claim that a black hole currently exists for us fails on two counts: firstly because no such black hole growth events have occurred in any of our past light cones and, secondly, because there are no frames which can claim otherwise for us or themselves.

    The typical response to this point is frame jumping by imagining ship A free-falling across an event horizon E with sufficiently low (survivable) tidal forces; however, this requires the existence of a black hole in the first place! We cannot use an imaginary black hole to prove the existence of theoretical black holes unless we are able to provide a theory of how they came to be in the first place. The problems faced by us on Earth would also exist for ship A; the existence of E could not be explained by any events in A's past light cone.

    At this point, Kruskal (or some other) coordinates are dragged out. Again, there is no point to this. Kruskal coordinates are only needed to analyze an existing black hole, and are not needed to discuss the birth of one. Additionally, no valid coordinate system (including Kruskal) can put growth events into the past light cone of any observer.

    I don't mean to have a contentious tone, but I am frustrated by my inability to find someone who can convince me that black holes aren't a grand example of the Emperor having no clothes.

    Oh, and MERRY CHRISTMAS! :)
  2. jcsd
  3. Dec 24, 2015 #2


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    The term "growth event" suggests that you're thinking of something that increases the mass of the black hole and hence its Schwarzschild radius. However, there are no such events in the Schwarzschild spacetime because it is static. Instead, when we talk about something falling through the event horizon of a Schwarzschild black hole, we're implicitly taking the mass of the infalling particle to be zero compared with that of the black hole so that the particle crosses the event horizon without (measurably) increasing the Schwarzschild radius or affecting the static spacetime around the black hole. That is, the particle crosses the event horizon without producing a "growth event"; this is a really good approximation, valid and useful for a wide range of real physical problems.

    Not as long as you're talking about the Schwarzschild spacetime. It doesn't have "growth events" at all so of course you won't find any of these in any past light cones and of course this will be the case no matter what coordinates you use.

    However, if you are considering processes in which infalling objects increase the mass and radius of the black hole, then you can no longer use the approximation that the infalling mass is near-as-no-never-mind zero, and the Schwarzschild spacetime is not a solution of the Einstein Field Equations under those conditions. Instead, you have to use something like the Oppenheimer-Snyder spacetime, in which the mass of the black hole changes over time and "growth events" can and do appear in the past light cone of outside observers.

    By Birkhoff's theorem, you'll end up with something that behaves like an eternal Schwarzschild black hole once the collapse is complete.
  4. Dec 25, 2015 #3


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    I believe we already had a very long thread on this, I'm not sure if there's a lot of point in repeating it in detail. I'll make the same general observation I made last time, mostly for the benefit of other posters who are curious about the issue. Consider Zeno's paradox, where Achilles (a fast runner) is chasing the tortise (a slow walker), where the tortise has a head start. Every time Achilles cuts the distance from him to the tortise in half, Zeno increments his time counter.

    Zeno never assigns a finite number to when Achilles reaches the tortise. But I think most people would agree that Achilles does catch up with the tortise. (I'm nor sure about R J Berry), and that the issue is with Zeno's timekeeping - his system doesn't assign a number (the time) to every event that happens, this doesn't mean that the event 'doesn't happen', rather, it means that Zeno doesn't assign a number to it.

    The analogy with the black hole case is that Zeno is keeping Schwarzschild coordinate time, and there's no number that can be assigned to the Schwarzschild coordinate time for when the object (Achilles) reaches the event horizion (the tortise). The detailed analysis of the similarity is in that other, very long thread. If there's any interest in it, I'll dig up the URL. As an overview, we can say that according to a clock carried by Achilles (the object), the time reading on that clock when it reaches the event horizon is finite, and Achilles sees the event happen, since he's there, so it is at least misleading (and I would argue that it's basically wrong) to claim that the object never does reach the event horizon.
  5. Dec 25, 2015 #4


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    We've had many long threads on this. The root of the problem is that people insist on trying to reason about black holes using ordinary language instead of math. Words like "perspective", "existence", "present", etc. are used as though they have precise definitions that can be used as the basis for logic, when in fact they're just vague ordinary language terms that simply do not justify the logical burden that posts like the OP of this thread attempt to put on them.

    The math is completely unambiguous: there are solutions to the Einstein Field Equations in which event horizons and black hole regions are present, and the physical meaning of those regions is perfectly clear and has been discussed numerous times already. Thread closed.
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