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I need to compute the linearised Einstein Equations around a fixed metric $g_{\mu \nu}$ which is not the flat metric.

Someone knows some Mathematica package or some review that can help me?

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I recommend this one Efficient tensor computer algebra for Mathematica. Here is a related question Differential geometry add-ons for Mathematica. You could start with this answer How to calculate scalar curvature Ricci tensor and Christoffel symbols in Mathematica? and then exploit new tensor capabilities in Mathematica 9. –  Artes Nov 8 '13 at 10:28
    
@Artes You could make that into an answer (reduce unanswered count). There's not much more to say here. –  Szabolcs Jan 9 at 20:03
    
@Szabolcs It should be elaborated a bit and I don't have enough time right now but I'll try to provide an answer on Sunday or Monday. –  Artes Jan 9 at 20:13
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