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Take the Kerr black hole and consider an infalling observer, say equatorial and with zero initial angular momentum for the sake of simplicity. Using the standard metric in Boyer Lindquist coordinates I think the worldline spirals around the horizon an infinite number of times as it asymptotically approaches it at $t \rightarrow \infty$. On the other hand I think the proper time for the observer to cross the horizon is finite. So my question is, does such an observer see the surrounding universe rotating around? And if so, then do they see the distant stars rotating around a finite number of times before they cross the horizon?

This is a question about literally seeing, i.e. receiving light from the stars. This light also spirals around the horizon in Boyer Lindquist coordinates as it falls towards the horizon. This makes me want to guess that the light received by the observer makes them see a finite number of rotations of the distant stars about them, and perhaps quite a small number like none at all. Anyway that is my question.

Andrew Steane
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    Have you seen this answer and in particular this link in it? – A.V.S. Aug 12 '21 at 06:21
  • @A.V.S. thanks very much this was most helpful, though I still don't have a clear statement of any apparent motion or lack of it for the distant stars (the images show snapshots and it is not quite clear how the line of sight is being set up, i.e. whether the observer is entirely inertial) – Andrew Steane Aug 12 '21 at 08:49

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