Are you sure? Can you describe, visually using the famous gravity well example, the central massive object rotating on an axis with a small object in a stable (non-inspiralling over the course of thousands or more revolutions) polar (or indeed any arbitrary nonequatorial) orbit about it?
One might compare your visualization with results from Gravity Probe B, which had an orbital inclination of 90.007 degrees, or Juno, which continues to have have this fun polar orbit (90.000 degree inclination) around Jupiter: https://en.wikipedia.org/wiki/Juno_(spacecraft)#/media/File:... (animated). Jupiter's mass and angular momentum ("J") parameters are, relevantly, greater than Earth's; additionally, GPB's was nearly circular, while Juno's is very highly elliptical.
I'm also curious about how you visualize -- using the gravity well example -- an extremely elliptical orbit even with J=0 and orbital inclination=0 -- one that alllllmost grazes the surface of the central object at closest, and at farthest is light-seconds away in effectively flat spacetime.
I'm not saying it can't be done, or even that you cannot do it. I just think it's hard -- I can't do it, or perhaps won't do it because I think it's easier to reach for an approximate solution of the Einstein Field Equations (and if one takes the mass of the small body to some unignorably higher level, through effective one-body methods). Others might reach for gravitoelectromagnetism. Others have some other favoured post-Newtonian or numerical method. Solve first, then grind out some useful visualization. But if you can successfully visualize first and extract a solution from that, with any sort of generality, then I'm honestly interested.
One might compare your visualization with results from Gravity Probe B, which had an orbital inclination of 90.007 degrees, or Juno, which continues to have have this fun polar orbit (90.000 degree inclination) around Jupiter: https://en.wikipedia.org/wiki/Juno_(spacecraft)#/media/File:... (animated). Jupiter's mass and angular momentum ("J") parameters are, relevantly, greater than Earth's; additionally, GPB's was nearly circular, while Juno's is very highly elliptical.
I'm also curious about how you visualize -- using the gravity well example -- an extremely elliptical orbit even with J=0 and orbital inclination=0 -- one that alllllmost grazes the surface of the central object at closest, and at farthest is light-seconds away in effectively flat spacetime.
I'm not saying it can't be done, or even that you cannot do it. I just think it's hard -- I can't do it, or perhaps won't do it because I think it's easier to reach for an approximate solution of the Einstein Field Equations (and if one takes the mass of the small body to some unignorably higher level, through effective one-body methods). Others might reach for gravitoelectromagnetism. Others have some other favoured post-Newtonian or numerical method. Solve first, then grind out some useful visualization. But if you can successfully visualize first and extract a solution from that, with any sort of generality, then I'm honestly interested.