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If you fell into a black whole with an accretion disc, but orthogonal to the plane of the disc - would you ever meet the disc?

I'm not asking whether you survive long enough, and obviously we assume that the disc has some non-zero width to avoid boring mathematical artifacts.

My intuition would say that it would look as if the disc would come towards me from all sides (spaghettification), but I'd like that confirmed or corrected by people who know about this properly.

As an add-on it would also be interesting to indeed deliberate if the cause of death would be due to heat first or that the curvature tears you to a line.

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Suppose we ignore any interaction between the infalling object and the accreting matter (jets, etc). In the Kerr solution for an eternal rotating black hole, an object falling along the axis of symmetry never quite reaches the equatorial plane, not even from its own perspective. Before reaching the equatorial plane, the object turns around and falls back out into another part of the extended spacetime (not visible to hovering bystanders who watched the object fall in), and then it turns around and falls back in again (in yet another part of the extended spacetime), and so on. This is described in the book by O'Neill (1995), The Geometry of Kerr Black Holes.

Real black holes are not eternal, because they form by gravitational collapse. This might qualitatively change the picture described above; I don't know, and one of the replies to the following question suggests that the answer might be unknown:

Spacetime diagram of a collapse of a rotating star

This answer also ignores quantum effects, which might also completely change the picture.

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  • $\begingroup$ Wow, I didn't expect rotation to change the picture this dramatically. Really my question was meant to be about the case of a non-rotating black hole (let's say the accrection disk formed just recently and the black hole isn't yet rotating much). I'm wondering if the intuition that the discs matter comes closer (which would be correct if everything just falls towards a point) is still correct then. $\endgroup$
    – John
    Commented Dec 24, 2018 at 13:22
  • $\begingroup$ @John Ah, okay. Without guessing, I'm not sure what the infalling accretion disk would look like to an infalling observer, even for a non-rotating black hole. I suppose it boils down to a curved-spacetime ray-tracing problem, to figure out which lightlike geodesics emitted from the accreting matter end up intersecting the observer's geodesic before impact. Interesting question. $\endgroup$ Commented Dec 24, 2018 at 15:24
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If you came in perpendicular to the ac creation disk, there is a good chance that you would be blasted by one of the jets spewing from the poles. Furthermore, if you are approaching a supermassive black hole, the effects of spagettification won't be noticeable until you have already journeyed inside the event horizon.

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  • $\begingroup$ Yes, but let's ignore the jets for the first and more interesting topological part of the question. And also yes, I expected that meeting the accretion disk's matter happens past the event horizon, although in general maybe that depends on it's width and the mass as you point out. $\endgroup$
    – John
    Commented Dec 23, 2018 at 8:39

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