I am a new user and have so far figured out how to calculate quantities with explicitly defined metrics (schwarzschild, kerr etc.) What I want to ultimately do is define a generic metric with undetermined functions. say (-f0(r,theta) dt ^2 +f1(r,theta) dr^2...) and calculate quantities like Ricci Tensor or the Einstein Tensor and set certain components of those to zero and then solve the resulting PDE. Could someone point me to the best way to do it?
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$\begingroup$ The Einstein equations are PDEs coupled to each other and more often than not, impossible to solve analytically except for special/trivial cases involving lots of symmetry. Unless you provide us with a specific metric/line element and concrete Mathematica code that troubles you, I'd say this is a mathematics question. If you want to see numerical solutions to the Einstein equations, please see the Einstein Toolkit code: einsteintoolkit.org $\endgroup$– Hans OloCommented Nov 25, 2022 at 19:44
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$\begingroup$ A mathematica code that can write down the Einstein equations for arbitrary given metrics (but not necessarily solve them) is the RGTC package by the late Prof. Bonanos, see here for some updated info on where to find the code: mathematica.stackexchange.com/questions/241409/… $\endgroup$– Hans OloCommented Nov 25, 2022 at 19:46
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