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Schwarzschild radius for non-rotating black hole

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