to obeys
P~hab = 0, (3-37)
gab ab = 0, (3-38)
which is known in the literature as the ingoing radiation gauge (IRG), an unfortunate
name because ingoing radiation is carried by 1" and Equation 3-37 tells us that the metric
perturbation is completely orthogonal to 16. Thus there is only outgoing radiation in the
ingfoingf radiation gauge! Obtaining the gauge conditions in Equations 3-37 and 3-38 is
more natural in the approaches of Cohen and K~egeles [20] and Stewart [21]. One startling
aspect of the gauge conditions is that there are five of them. This being the case, we must
be concerned about the circumstances under which the metric perturbation in the IRG is
well-defined. This is the subject of the next chapter.
Our derivation began with the Teukolsky equation for Ie',, Had we instead started
with the Teukolsky equation for 4,/3 ~4, We WOuld be led to a metric~ perturbation
in terms of a Hertz potential, 9', that satisfies the Teukolsky equation for Ie',, The
resulting metric perturbation and gauge conditions are then simply the GHP prime of
Equations 3-35, 3-37 and 3-38, respectively. In this case, the metric perturbation exists
in the so-called outgoing radiation gauge (ORG). For the remainder of this work, we will
focus our attention on the IRG metric perturbation, but all the results hold for the ORG
perturbation as well.
On a final note we remark that the Teukolsky equation for Ie',, (Equation 3-25)
actually exists in the more general type II spacetimes, without its companion for ~4- I
this case, Wald's method also leads to metric perturbation (in the IRG, no ORG exists
here), with a potential, 9, satisfying the adjoint of Equation 3-25, which, in this instance,
is not the equation for the perturbation of #4-