= Radial null geodesics of the Vaidya metric
{title2=$v=\mathrm{const},\quad dr/dv=(1-2M/r)/2$}
= Radial null geodesic of the Vaidya metric
{synonym}
The two radial <null geodesic> families are $v=\text{constant}$ and $dr/dv=(1-2M(v)/r)/2$. The first has affine radius, while the second has tangent $k=\partial_v+(f/2)\partial_r$ obeying $\nabla_kk=(M/r^2)k$, so advanced time is generally a nonaffine parameter. An <affine parameter> $\lambda$ for the outgoing family satisfies $d\log(dv/d\lambda)/dv=-M/r^2$.
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