where 1" is aligned with the repeated PND of the background Weyl tensor. If n" rather
than 1" is a repeated PND, we instead define the outgoing radiation gauge (ORG) by
nahab = 0, (4-3)
gab ab = 0. (4-4)
In type II background spacetimes, only one or the other of these options exists (IRG
or ORG), whereas in Petrov type D background spacetimes, there is the possibility of
definingf both gauges. For the remainder of this work we focus on the IRG. Results for the
ORG can be obtained by making the replacement la t qn
Equations 4-1 translate into algebraic conditions on the components of the metric
perturbation. We will refer to the four conditions in (4-1) as the 1- & gauge conditions.l In
terms of the tetrad components of the metric perturbation, these gauge conditions read:
hit = 0, hin = 0, him = 0, him = 0. (4-5)
The condition in Equation 4-2 will be referred to as the trace condition and can be
expressed in terms of the components of the metric perturbation as hi, kmm = 0, which,
when Equation 4-5 is imposed, simply reads
hmm = 0. (4-6)
Because the IRG constitutes a total of five conditions on the metric perturbation, instead
of the four one might expect for a gauge condition, it is necessary to ensure that the
extra condition does not interfere with any physical degree of freedom in the problem,
] Recently, when applied specifically to the Schwarzschild spacetime, these conditions
were given a geometrical interpretation, and referred to as light-cone gauge conditions [59],
though they are not the conditions originally introduced for gravitation with that name
[60]. It may well be that this description is suitable more generally, although presumably
without the specific geometrical interpretation of [59].