I have defined a manifold, along with a metric and its perturbation. Using the Perturbed[] command I've been able to compute the perturbation of the Ricci tensor to all orders, but how do I actually 'plug in' a background metric, and explicitly carry out the derivatives and all summations? It's going to be quite messy, so is there a way to specify an ansatz for the perturbation?
I tried using Bloomfield's tutorial on perturbation theory with xAct on xAct.es but it only goes as far as using Perturbed[].