Schwarzschild Radius Derivation: Is it Possible Classically?

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Is it possible to derive r=GM/c^2 classically(as in Newtonian gravity) without using eeinstein field equation?
 
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You can set the escape velocity to ##c## and find this radius immediately in Newtonian gravity: ##c=\sqrt{\frac{2GM}{r}}\rightarrow ~r=\frac{2GM}{c^2}## however, what this radius means in Newtonian gravity is not the same as what it means in GR.