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Can you see light from ring singularity from inside the Cauchy Horizon? In between 2 horizons space and time coordinate swaps places, so the inside region lies at the future. But after crossing Cauchy time starts behaving normally, so light from the ringulaty should be visible to an observer in this region.

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  • $\begingroup$ spelling: "ringularity" - quite good ;) $\endgroup$
    – m4r35n357
    Oct 4, 2021 at 10:27
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    $\begingroup$ You shouldn't really get hung up with the ring singularity, anything after the cauchy horizon is an unphysical mathematical artificat. In fact, there are infinitely many things that may happen beyond the Cauchy horizon, and the ring singularity is merely one of them, that we get when we assume the metric is analytic. This assumption is unphysical, because information about a given point can give you the full spacetime configuration, and that is not go well with notions like causality. $\endgroup$ Oct 11, 2021 at 21:13

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The answer is yes in the technical sense that in the Kerr geometry, there are lightlike geodesics that originate at the singularity and pass through any point inside the inner horizon (Cauchy horizon).

But it's a vacuum solution, so there's no light to see, and also no you to see it. There's evidence that perturbing it by adding any matter (even just the matter that initially collapsed to make the hole) leads to a spacelike singularity just outside the inner horizon, and no interior with a ring singularity. So realistic spinning black holes probably have the same causal structure as Schwarzschild black holes: you can't see the singularity because it's in the future.

(arXiv:1907.05292 is an interesting review article about this and other aspects of black hole interiors.)

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If you want a representation of what an observer can actually see "inside" a black hole (hint: it is probably more complicated than you think!), your options are very limited!

A good place to start with is Andrew Hamilton's Home Page. Unfortunately he has not been able to provide the software for you to reproduce his work.

If you want to be more "hands on" and make your own views, then I think your only option is David Madore's page. He provides a single-file c program that creates PPM images, but you will need to compile it yourself! His black holes tutorial is very good IMO, and I would strongly recommend reading it.

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