CHAPTER 4
THE EXISTENCE OF RADIATION GAUGES
In the previous chapter, it was seen that the perturbations of the Weyl scalars lead
quite naturally to metric perturbations in the radiation gauges, (seemingly over-) specified
by five conditions. In this chapter we will explore the precise circumstances under which
one can impose all five of these conditions. This will require us to examine the perturbed
Einstein tensor, which presents the need to integrate some of the components. For this, we
will appeal to a coordinate-free integration technique based on the GHP formalism, due
to Held [45, 56]. The generality of these methods allow us to prove the result for a much
broader class of spacetimes than we have encountered so far, namely, Petrov type II, which
we will see is the largest class of spacetime for which the radiation gauges are defined. We
begin with a more thorough discussion of the radiation gauges and their origin. 1\ost of
this chapter is taken from published work [57].
4.1 The Radiation Gauges
The in going radiation gauge (IR G) is a crucial ingredient for the reconstruction of
metric perturbations of Petrov type D spacetimes from curvature perturbations. They first
appear, unexplained, in the work of Cohen and K~egeles [58] (for perturbations of Petrov
type II spacetimes) and Cht!. I.!, ~.--- 1:! [54] (who considered perturbations of Petrov type D
spacetimes), but the work that comes closest to our contribution in describing their origin
is that of Stewart [21], again for the more general case of type II spacetimes.
In type II background spacetimes, the IR G is defined by the conditions
P~hub = 0, (4-1)
gab ab = 0, (4-2)