# Schwarschild Metric from Kepler law

Can we redrive Schwarschild metric from Kepler's law without assuming General Relativity?

But this is not really a derivation because it assumes that the $$r$$ in Kepler's law is the same as the Schwarzschild $$r$$ coordinate, and this is not the case. It also assumes that the $$t$$ in Kepler's law is the same as the proper time, and again this is not true.
The result is a coincidence due to the way the Schwarzschild $$r$$ coordinate has been chosen There are several such coincidences. For example we have the coincidence that the event horizon position is the value of $$r$$ for which the Newtonian escape velocity is equal to the speed of light, and again this is due to the way the Schwarzschild $$r$$ coordinate has been chosen.