- #1

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$$\textrm{d}s^2= \left(1-\frac{2m}{r}\right)\textrm{d}T^2-\left(1+\frac{2m}{r} \right)\textrm{d}r^2-\frac{4m}{r}\textrm{d}T\textrm{d}r=0.$$

$$\textrm{d}\theta=\textrm{d}\phi=0$$

My biggest challenge is to understand the question. What counts as the equation for a radial in-going null geodesic. Is it the line element that's the equation or is it the geodesic equation?