quantities through gauge invariant entities, Lousto thus succeeded in reconstruction
perturbations of Schwarzschild in a way that includes sources.
Lousto actually uses both I',, and #'4 in his construction. For concreteness and for
access to a vast body of prior experience, Lousto also chose to work in a gauge known as
the RW gauge. Note that Equations 1-21 and 1-22 are only valid in the IR G. However,
Ie', and #'4 are eaSily expressible in terms of an arbitrary metric perturbation, which allows
them to be written in terms of the RW variables for any choice of gauge. In the RH
gauge, I',, and #'4 become algebraic in the even parity sector and first order operators in
the odd parity sector. To provide enough conditions to solve for all the components of
the metric perturbation in terms of the Weyl scalars, Lousto must turn to the Einstein
equations (with sources), also in the RW gauge. It is in this way that reconstruction with
sources is accomplished.
The identification of gauge invariant quantities, beyond I',. and #'4, iS Virtually
nonexistent in the K~err spacetime and as pointed out several times before, the angular
decomposition there is not as robust as that available in spherically symmetric backgrounds.
In short, Lousto's work is quite notable for its inclusion of sources, but its reliance on RW
tools and techniques make it difficult to see how to extend the method to the K~err
background.
1.4 This Work
motivated by the success of spin coefficient formalisms in describing perturbations of
type D spacetimes and the incompleteness of current approaches, this dissertation presents
a new framework for perturbation theory that exploits the best features of both standard
treatments of perturbation theory and those based in the methods of a spin coefficient
formalism. As we will see, a natural feature of this formalism is that it applies to general
algebraically special spacetimes with little extra effort. Though our framework is quite
general and provides a new means of understanding perturbations of a wide variety of
spacetimes, we will keep our focus more narrow than that. In particular, the applications