Results from paper I

Here are some of the results that I developed while doing the work that went into this paper; a lot of this stuff has been presented elsewhere at this point, so this page is kept mostly for historical reasons. On some of these pages I use an alternate inclination angle iota' which, in the end, I didn't really end up using very much. It is defined via

Tan(iota') = (dtheta/dtau) / (dphi/dtau) ,

evaluated at the equator. iota' is the angle at which infinitely distant observers see the orbit cross the equatorial plane. The above expression evaluates to

Tan(iota') = Q^½ / [L_z + a (2r E - a L_z)] .

Note that iota and iota' are identical for non-spinning black holes, and approach one another in the weak-field limit.

Here are results for particular orbits.

Orbit of black hole with a/M = 0.95, at radius r/M = 7, inclination angle iota = 62.43 degrees, iota' = 57.71 degrees. Results.

Orbit of black hole with a/M = 0.05, at radius r/M = 7, inclination angle iota = 60.17 degrees, iota' = 59.90 degrees. Results.

Orbit of black hole with a/M = 0.95, at radius r/M = 100, inclination angle iota = 60.05 degrees, iota' = 59.95 degrees. Results.

Orbit of black hole with a/M = 0.05, at radius r/M = 100, inclination angle iota = 60.00 degrees, iota' = 60.00 degrees. Results.

Radiation reaction changes the values of r and iota, driving some orbit (r₁, iota₁) to a new orbit (r₂, iota₂). I have just begun exploring this effect and have put together a very sketchy picture of how this works:

Radiative evolution of orbits around a black hole with a/M = 0.8. Results.

Last modified 18 July 2000.