= Coordinate invariance of the Schwarzschild photon radial potential
{title2=$V_{\rm eff}(r)=(1-2\mu/r)/r^2$}
A stationary time-coordinate change $t'=t+F(r)$ leaves both the <areal radius> and the time-translation <Killing vector field> unchanged. The conserved <Killing energy> and <angular momentum> of a <null geodesic> therefore yield the same radial equation in either chart, $\dot r^2+h^2(1-2\mu/r)/r^2=c^2k^2$. The <effective potential> and radial <turning points> agree, even when the coordinate time velocities and horizon regularity differ.
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