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To be able to move around the black hole, it may be possible to create a fudge to avoid implementing all of general relativity.
The disc breaks into two when viewed from the front, but is just a single disc when seen from above or below. So using phi for the azimuthal angle (east-west in the disc plane), and theta for the polar angle (north-south from North Pole to South Pole), it may be possible to create two discs, one curving downwards, and one upwards that both depend on the theta-coordinate for their shape, and on the phi-coordinate for their orientation so the largest separation between the discs is always behind the black hole from the viewing location. Going from North Pole to South Pole, the two discs start in the same plane, then break apart farther and farther until the equatorial plane is reached, and then merge again at the South Pole.
Since the two discs look different at all angles except at the North and South Pole, and in the equatorial plane, the modelling would have to be independent for both discs depending on theta, and not symmetrical with respect to the equatorial plane.
This would have to be rendered for all players individually based on their own theta- and phi-coordinates. Clearly this is still not trivial.