On the Ricci tensor of non-stationary axisymmetric space-times

We recalculate the Ricci tensors of non-stationary axisymmetric space-times originally calculated by Chandrasekhar, and we find that in the linear regime there are some common factors that did not appear in the original results. We also find some discrepancies in the non-linear terms. However, these discrepancies do not affect the well-known results concerning linear perturbations of a Schwarzschild black hole.