The Carter Constant for Inclined Orbits About a Massive Kerr Black Hole:
  near-circular, near-polar orbits
  In an extreme mass-ratio binary black hole system, a non-equatorial orbit
will list (i.e. increase its angle of inclination, {\iota}) as it evolves in
Kerr spacetime. The abutment, a set of evolving, near-polar, retrograde orbits,
for which the instantaneous Carter constant (Q) is at its maximum value (Q_{X})
for given values of latus rectum (l) and eccentricity (e), has been introduced
as a laboratory in which the consistency of dQ/dt with corresponding evolution
equations for dl/dt and de/dt might be tested independently of a specific
radiation back-reaction model. To demonstrate the use of the abutment as such a
laboratory, a derivation of dQ/dt, based only on published formulae for dl/dt
and de/dt, was performed for elliptical orbits on the abutment. The resulting
expression for dQ/dt matched the published result to the second order in e. We
believe the abutment is a potentially useful tool for improving the accuracy of
evolution equations to higher orders of e and l^{1}.
