Schwarzschild Radius Derivation: Is it Possible Classically?

[TimeRip496]

Is it possible to derive r=GM/c^2 classically(as in Newtonian gravity) without using eeinstein field equation?

 

[Matterwave]

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.