the help of GHPtools) to the Teukolsky equations. They are
[( -4p )(' ')- 8 4 -f'(' 7) S'_,', = 4xrTo, (3-25)
[(D'~~~~~~~~ p '( ) 8 7 )( )-3']4 T4, (3-26)
where, in terms of the components of the metric perturbation
,,- (8 -T')8 -f')zz (P p)(P p)hmm
[(P P)(B 2r') +(di 7')(> 2p)]him (3-27)
(D' p'( 27)h + (p' 7)(p' 2p')]h~), (-8
and where the parentheses, (), around the tetrad indices denote symmetrization. It
is both interesting and important to note that, in the K~err spacetime, the coordinate
description of Equation 3-26 does not lead to the separable equation discussed in (I Ilpter
1 (Equation 1-17). To obtain a separable equation, an extra factor of --4/3" muSt be
brought in, resulting in the following expression:
[(p' p')(P + 3p) (a' -r)(a + 37r) 3/' _]1' _4/3 4 --4/;:3:34. (3-29)
Below we will see the same expression arising from very different considerations.
3.4 Metric Reconstruction from Weyl Scalars
The solutions of the Teukolsky equation lead quite naturally to a metric perturbation
in several different v- .--s. The original result, due to Cohen and K~egeles [20] used spinor
methods. Shortly after that, C'!,l~!!. i .---1:! [54] obtained essentially the same result
using factorized Green's functions. Some time later, Stewart [21] entered the game and
provided a new derivation rooted in spinor methods. Eventually, Wald [55] introduced a