I guess you need something like two pound signs to do math here, not a dollar sign. Also, there are a number of bad line breaks - Wordpress blogs are unforgiving when you hit the carriage return.Outside $r = 6m$, oscillations are stable.
Good idea! I went away and commented out the horizon calculations in my own minimal simulator (I started a thread for it but struggling to find it ATM!), and tried a fairly complex bound 3+1D orbit with a = 1.1 and a = 1.5. Both produced "valid" orbits. It seems on the face of it that the equations of motion do not care about the existence of horizons ;)What I'd really love to see is a study of orbits in a Kerr metric that describes a 'super-extremal' black hole, one with ##J^2 > M^2##. These could get pretty weird!