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I guess we can leave it to the imagination about what lies beyond that second horizon
Well, actually, we don't.https://youtu.be/4v9A9hQUcBQ
Episode of PBS Spacetime that goes on a journey through a Kerr black hole, its ringularity and back through while showing the journey on a Penrose diagram.http://www.madore.org/~david/math/kerr.html#videos
Simulations of various geodesics going through a Kerr black holehttps://jila.colorado.edu/~ajsh/insidebh/rn.html
A photorealistic simulation of a Reissner-Nordstrom black hole. Same structure, charge instead of centrifugal force spits observer back out. Here, you can get a feel for what the grids in the Kerr simulation are trying to show.
David Madore's program in the second link is very hard to use. The kerr-image program has to be recompiled to change the resolution of the output, and it cannot make videos and geodesics on its own. A different program has to be used to calculate the geodesics and the file output has to be split and fed into the program. Frames bigger than 50x50, like 1920x1080, take a while to render and a minute video would take days to render.
Andrew Hamilton's BHFS was used to create the Reissner-Nordstrom black hole simulation, and it should run real-time (or close enough) on modern systems. However, the graphical libraries the BHFS runs on have been abandonware for a while and Hamilton is unable to make the BHFS public. They explain that CU students have been unwilling to port the BHFS to newer libs, which is understandable:The BHFS is a complex code, with more than 100,000 lines of c and c++
These programs let you fly around a schwarzschild black hole, but the programs are limited in their capabilities:https://ebvalaim.pl/en/black-hole-simulator/http://spiro.fisica.unipd.it/~antonell/ ... hild/live/
It would be very cool if SE could become the first full-scale public project to simulate relativity and geodesics within black holes - and in real time.