to account for. Wald's theorem [16] actually specifies two other types of perturbations
that I',, and d'4 cRallOt ROcount for. perturbations towards the accelerating C-nietrics and
perturbations toward the NITT solution. In the work of K~eidl, et. al. [69], where they
concerned themselves with a static particle in the Schwarzschild geometry, it was found
that the spacetinle on the interior differs front that on the exterior by a perturbation
towards the C-nietrics. This makes physical sense because a static particle is not on a
geodesic of the Schwarzschild spacetime and thus requires acceleration to keep it in place.
Though we have no obvious physical reason to expect these perturbations for circular,
equatorial orbits of the K~err geometry and evidence front the Schwarzschild calculation
-II- -_ -r ;they should not contribute, we have not yet proven a result either way.
Finally, one question that we have overlooked entirely is the question of the stability
of a thin shell. In the Schwarzschild background, this problem has been solved by Brady,
Louko and Poisson [77], who showed that a thin shell is stable and satisfies the dominant
energy condition almost all the way up to the location of the circular photon orbit (located
at r = 3M~). There are no such results to report on for the K~err spacetinte. The closest
thing to a step in this direction is the work of 1\usgrave and Lake [78], who consider the
matching of two K~err spacetintes with different values of mass and angular montentunt.
Unfortunately, these authors were forced to resort to the slow rotation approximation
discussed earlier. Strictly speaking, without knowledge of the existence of a stable shell
of matter sufficiently close to the black hole, we are left to question the validity of our
procedure. This is a problem we leave for future work.