In rotating black holes, the singularity is believed to be a ring or torus, unlike the single-point singularity of a non-rotating black hole.

Topological change - Imagine we have two distant black holes with negligible spin orbiting each other: they can be approximated as Schwarzschild black holes and their singularities are point-like. After a long time, they will be in a close inspiral phase, till they merge and give rise to a rotating black hole. A topological change should be expected, from two disconnected singularities to a connected singularity shaped like a ring.

Similarly, when two rotating black holes merge and stabilize, the two disconnected ring singularities would again give rise to a single ring (apparently, we can not have distinct singularities in a stable black hole).

Main question: has this process ever been theorized, simulated or observed?

Related curiosities - Are other geometries (e.g. a torus?) possibly realized during the process? Given two different angular momenta vectors of the two original black holes, with the original black hole ring singularities lying in their own respective planes, could a newly forming ring singularity be a closed loop but have ripples above and below the final plane of the new singularity ring before it stabilizes? Could a newly forming and stabilizing ring singularity form geometries more complex than a ring?

Possible observation and references - I know that LIGO-Virgo data during the ringdown period of black hole mergers are starting to reveal more information, see also this question. If anyone has a reference to published work or insight into the dynamics of the topological change (maybe animations from simulations?), it would be greatly appreciated! I have seen animations showing gravitational waves emission during the inspiral, but I have never seen animations of the two disconnected singularities merging in a ring.

Edit: some specialistic theoretical results are listed in Theoretical solution to binary black hole merger based on Hawking and Ellis. Is there, to date, a consensus or new ideas on how the topological change proceeds?

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    $\begingroup$ "In rotating black holes, either Kerr (uncharged) or Kerr-Newman (charged) the singularity is believed to be a one dimensional ring or torus, ... " There is no reason to actually expect this to be true for astrophysical black holes. The Kerr solution is known to be unstable at the inner horizon. There is no reason to believe anything beyond the inner horizon in the exact Kerr solution will appear in an astrophysical solution. $\endgroup$
    – TimRias
    Jul 2, 2021 at 7:57
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    $\begingroup$ Related: physics.stackexchange.com/a/176739/226902, physics.stackexchange.com/q/235867/226902 and physics.stackexchange.com/a/424253/226902 and this arxiv paper arxiv.org/abs/1606.00436 "Toroidal Horizons in Binary Black Hole Mergers" $\endgroup$
    – Quillo
    Feb 20, 2023 at 17:51
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    $\begingroup$ The arxiv preprint cited by Quillo did find a publisher (Physics Rev D) within 3 months. $\endgroup$
    – Edouard
    Feb 20, 2023 at 19:46


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