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Given a natural Hamiltonian,

$$H = \frac{1}{2} g^{\mu \nu}(x) p_{\mu} p_{\nu} + V(x)$$ and a general potential $V(x)$ I want to be able to find the coordinates, given an expression for $V(x)$, such that the Hamiltonian is separable.

I had previously asked a question here and got an answer, but am more interested in the specific case of a 4D psuedo-Riemannian manifold.

After some extensive google-ing I am coming up empty handed on resources. Can anyone recommend, or even provide an answer?

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