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I was reading some questions and answers about black holes and whether matter can actually pass through the apparent horizon, in particular this one:

How can anything ever fall into a black hole as seen from an outside observer?

It seems that the argument that matter slows down and never passes the apparent horizon is similar to Zeno's paradox Achilles and the tortoise. Due to the effects of the immense gravity a photon emitted by the matter travelling away from the black hole get red shifted and from its perspective takes longer to reach our hypothetical observer than if the black hole was not there. At some point it will take 10 times as long to reach us than normal, then there will be a point at which it takes 100 times as long, then 1000 times and so on. If you keep measuring infinitesimally smaller increments you can keep this progression going forever since at precisely the apparent horizon it will take a photon travelling exactly away from the black hole an infinite amount of time to reach us.

However, as far as I can see, all this remains true if the object accelerates towards the black hole as viewed from some outside time frame. Due to time dilation effects it will appear to an in-Universe observer that the object never quite reaches the apparent horizon yet it seems to me that an outside Universe observer would see the object pass through and merge with the mass at the centre of the black hole very quickly.

Are both views correct or does it not make sense to contemplate the Universe from outside the Universe? If we were able to measure the gravity of the object directly and separately from the remaining mass of the black hole would we be able to detect that the matter had indeed passed the apparent horizon?

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closed as unclear what you're asking by ACuriousMind, Kyle Kanos, LDC3, Jim, yuggib Jun 8 '15 at 18:35

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ @AcidJazz From inside the universe we are constrained by the effects that general relativity, etc. describe, i.e. time dilation, relative distances and so on. If we could place ourselves "just outside" the universe and observe what was happening in it in real time instead of waiting perhaps billions of years for photons to travel from point A to point B what would we see? My understanding is that although we can't directly observe matter enter a black hole because it appears to take an infinite amount of time to us, that the matter actually crosses the apparent horizon quite quickly. $\endgroup$ – CJ Dennis Jun 6 '15 at 11:45
  • $\begingroup$ What about gravity? Black holes lose energy via gravity. Isn't that information? By way of analogy, in maths there are imaginary numbers. Some problems which only have real answers can only be solved easily by using imaginary and complex numbers, which are very well defined and understood. Can we think about the Universe the same way? Let's remove ourselves from any frame that exists within our universe (but only slightly) and then observe the previously unobservable. Isn't this what physicists do when discussing the interior of black holes? Maybe think of it as a god's eye view. $\endgroup$ – CJ Dennis Jun 6 '15 at 12:09
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    $\begingroup$ It's not clear to me what your question is. What is this "outside time frame" you mention? What does "outside the universe" even mean? $\endgroup$ – ACuriousMind Jun 6 '15 at 14:43
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If you or or indeed any observer wants to make measurements of how some object moves we need to choose a coordinate system to do it. This isn't as complicated as it sounds. If I have a clock and a ruler then I can use this these to mark out a grid in space and time, then I can plot the trajectory of a falling object as a sequence of points, $(t, x, y, z)$, on this grid.

Pre General Relativity we could mark out a grid that filled all of spacetime in a nice regular fashion. You could do the same, and while your grid might not be lined up with mine it's a relatively simple transformation to make the two grids match.

What we discover when we learn General Relativity is that different observers can have radically different coordinates (I'm going to use the more general term coordinates rather than grids). This is what happens in the case of the black hole event horizon. If we're sat outside the black hole watching an object fall in then our coordinates cannot be matched up with the falling object's coordinates at the event horizon. At the event horizon our coordinate system has a coordinate singularity that means we can never observe the object cross the horizon. The coordinates used by the falling object have no such singularity, and the object will measure itself to cross the horizon and reach the centre of the black hole (and a messy death) in a finite and indeed very short time.

The problem with the universe is that it has no outside. All observers are by definition inside it, and their attempts to measure it are always restricted by the sorts of problems with coordinates that I've just described. What General Relativity gives us is a coordinate independant way to describe the universe, and this description is a mathematical object called the metric tensor (or just metric for short). The metric covers all of spacetime, and we can use it to calculate the trajectory of the falling object and see that it does indeed cross the horizon even though our coordinates do not allow us to observe it doing so.

So there is a sense in which there is a god's eye view that shows everything in the universe, but this is a purely mathematical object. No observer can ever see this structure directly, only through the lens of their coordinate system, and the coordinate system restricts the view.

With some spacetimes it is possible to embed the spacetime in a higher dimension. By this I mean the four dimensional spacetime can be represented as a hypersurface in five dimensions. A hypothetical five dimensional being could then have a god's eye view of everything in a four dimensional universe. But there's a problem. I suppose the obvious problem is that as far as we know no fifth dimension or five dimensional beings exist. But even if they did only some universes can be embedded in this way, and all the interesting universes cannot. If you're interested in more on this see the question Can a non-Euclidean space be descripted through an Euclidean space of higher dimension? So why use non-Euclidean?.

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  • $\begingroup$ You get the big green tick for understanding my question! Basically the god's eye view is imagining ourselves to be in the same frame as the object approaching the black hole, even though we can never observe it and survive! For we too would have to be inside the apparent horizon with no way of communicating our observations back home! But our imaginations are immune from a black hole's gravity! $\endgroup$ – CJ Dennis Jun 8 '15 at 11:23
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I think your considerations are led by the daily experience that what you see actually happens as you see it. However, this is an illusion. All you perceive are photons, but they can (1) take their time and (2) can be redshifted or absorbed.

Of course, the object quickly passes the event horizon (in its own frame it doesn't even notice the event horizon), but this is not observable -- that's why it's called an event horizon. It is hidden from the rest of the world by the enormous gravitational redshift (which reaches infinity at the horizon).

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I may be missing your point here, and apologies if I am, but how can we contemplate the universe from outside it? Even if that ever moves from the, to me anyway, currently purely philosophical/opinion type question to a definite physics based, engineering type solution, (if ever) how do we then communicate between universes? 

   Once matter crosses the event horizon, all information is lost to us, it cannot communicate back. My sincere apologies, I may be completely misunderstanding your point, but in General Relativity theory, crossing the event horizon, at no matter what speed it travels, makes no difference to the impossibility of communicating with it in any way.

Gravity is information in the sense that it tells you the mass of the black hole, but that's all, unfortunately. Think of it as a completely disorganised scrapheap, you know beforehand what it was you threw in , but after a whole other heap of more junk goes in, you can't find it so easily, in the black hole case, this is taken to the extreme. We only know the total mass, total rotation speed and total electric charge. No individual items stand out. As far as the interior of black holes goes, when have ideas, but that's all they are right now, ideas, no direct observations to test them

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