The Schwarzschild metric for an eternal non-rotating black hole is a special case of the Kerr metric for an eternal rotating black hole. But the Penrose diagrams for the maximal analytic extensions (MAEs) of these two spacetimes look qualitatively different from each other, as shown in sections 2.4 and 4.2 in https://arxiv.org/abs/gr-qc/9707012. Is MAE-Schwarzschild somehow still a special (or limiting) case of MAE-Kerr, despite this qualitative difference? Are there any simpler examples to illustrate this?
I understand that we don't expect these eternal black hole solutions to have direct relevance to astrophysics, but I would still like to understand this mathematical aspect of GR.
Since Penrose diagrams are a bit abstract, I'll add some spice to the question by relating it to the fates of infalling test-objects. When a test-object falls into a Schwarzschild black hole, it hits the singularity in a finite proper time. A test-object falling into a Kerr black hole along the axis of symmetry has a different fate. If I'm not mistaken (please correct me if I am), the infalling object never even reaches the plane of the ring singularity. Instead, it turns around and falls back out (by crossing a white hole horizon in the MAE), then falls back in (by crossing a different BH horizon in the MAE), then falls back out, then back in, and so on forever. This is qualitatively different than the fate of the test-object in the Schwarzschild case. Can the behavior of the test-object in the the Schwarzschild case be understood as a special (or limiting) case of the behavior of the axially-falling test-object in the Kerr case?