Simplifying Linearized Equations in GR Using Gauge Transformations

[Psychosmurf]

I need some help with a derivation in GR.

The linearized field equation in GR is:

G_{ab}^{(1)} = - \frac{1}{2}{\partial ^c}{\partial _c}{{\bar \gamma }_{ab}} + {\partial ^c}{\partial _{(b}}{{\bar \gamma }_{a)c}} - \frac{1}{2}{\eta _{ab}}{\partial ^c}{\partial ^d}{{\bar \gamma }_{cd}} = 8\pi {T_{ab}}

How would I use the gauge transformation

{\gamma _{ab}} \to {\gamma _{ab}} + {\partial _b}{\xi _a} + {\partial _a}{\xi _b}

to simplify the linearized equation to:

{\partial ^c}{\partial _c}{{\bar \gamma }_{ab}} = - 16\pi {T_{ab}}?

EDIT: I should also mention:

{{\bar \gamma }_{ab}} = {\gamma _{ab}} - \frac{1}{2}{\eta _{ab}}\gamma

\gamma = \gamma _a^a

and

{g_{ab}} = {\eta _{ab}} + {\gamma _{ab}}

 

[Psychosmurf]

Nvm. I figured it out.