How do I apply weak field approximation to the Einstein field equation?

[Das apashanka]

Actually from the Einstein field equation I am trying to compute the R₀₀ component and get at a point
R₀₀=k(.5Tg₀₀-T₀₀)
where,T=g^αβT_αβ
now I am trying to apply the weak field approximation ,how will I proceed?

 

[haushofer]

Again: give us more background. Is this homework? Reaearch? What books are you using?

Applying weak fields means you split up the metric as a background plus fluctuation, and neglect all the fluctuation terms of order 2 and higher. But this is again a textbook result and can be found in wvery textbook on GR, so what's precisely the problem you encounter?