## Schwarzschild radius for non-rotating black hole

Generated by the Physics Derivation Graph.

https://en.wikipedia.org/wiki/Derivation_of_the_Schwarzschild_solution

Raise both sides of Eq. \ref{eq:1044984} to $$2$$; yields Eq. \ref{eq:2478510}. $$v_{\rm escape}^2 = 2 G \frac{m}{r} \label{eq:2478510}$$ Change variable $$v_{\rm escape}$$ to $$c$$ and $$r$$ to $$r_{\rm Schwarzschild}$$ in Eq. \ref{eq:2478510}; yields Eq. \ref{eq:5459812}. $$c^2 = 2 G \frac{m}{r_{\rm Schwarzschild}} \label{eq:5459812}$$ Multiply both sides of Eq. \ref{eq:5459812} by $$r_{\rm Schwarzschild}$$; yields Eq. \ref{eq:9932666}. $$r_{\rm Schwarzschild} c^2 = 2 G m \label{eq:9932666}$$ Divide both sides of Eq. \ref{eq:9932666} by $$c^2$$; yields Eq. \ref{eq:9994959}. $$r_{\rm Schwarzschild} = \frac{2 G m}{c^2} \label{eq:9994959}$$