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
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