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I need to evaluate the Einstein tensor/ Ricci tensor and others in a perturbed metric. Suppose my metric is

$g_{ab} =\eta_{ab} +h_{ab}$, where $\eta$ is the Minkowski metric, and $h$ is a small perturbation. I want to find the first order correction to the aforesaid metrics.

Is there any software/package that is capable of doing this kind of symbolic computations?

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  • $\begingroup$ xAct $\endgroup$
    – Noone
    Commented Jan 28, 2021 at 18:11
  • $\begingroup$ You can write this sort've thing quite easily into Mathematica or Maple $\endgroup$
    – Eletie
    Commented Jan 28, 2021 at 18:26
  • $\begingroup$ physics.stackexchange.com/q/104805/226902 (cadabra) $\endgroup$
    – Quillo
    Commented Oct 10, 2023 at 21:07

2 Answers 2

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While these sorts of things are obviously 'to taste', my preferred two are:

Mathematica with the xAct package with the xTras addon. There is a useful tutorial on e.g. expanding perturbatively around AdS here.

The second option is to use Cadabra. This is a wonderful program where everything is input and rendered directly in $\LaTeX$, and is very intuitive to a field theorist (it is built for supergravity calculations). This takes a bit of getting used to if you're a Mathematica fan, but in my opinion, it's worth it. It helps if you know a basic amount of python, but you barely need much.

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I suggest you explore Sagemath, here you have some examples to browse.

https://sagemanifolds.obspm.fr/examples.html

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