gravity - Escape velocity for an arbitrary metric in General Relativity

It's a known calculation how to derive the escape velocity of a system following the Schwarschild Metric. It comes out to be, if I am not wrong $$v = c\sqrt{2GM/Rc^2 - (2GM/Rc^2)^2}$$

So, is there a general method of finding out the escape velocity for a given general metric, without assuming any symmetry considerations?

A mathematical help would be highly appreciated