Can you please incorporate all these equations together with my Micha Solution Equation 

−Rμν​+21​gμν​R−Λgμν​=−κTμν​−κΔTμν​

Rμν​−21​gμν​R−(Λ+ΔΛ)gμν​=κTμν​+κΔTμν​

Rμν​−21​gμν​R+Λgμν​=−κ(Tμν​+ΔTμν​)

Rμν​−21​gμν​R+Λgμν​=κ(Tμν​+ΔTμν​+ΔTμν′​)