Reconstructing Vaidya mass from a radial null geodesic ($M(v)=\frac{1}{2}{r}_0(v)(1-2r_0^{\prime }(v))$)

An outgoing radial null geodesic of the Vaidya metric prescribed as $r=r_0(v)$ determines the mass along that curve by $M(v)=r_0(v)(1-2r_0^{\prime }(v))/2$. This inverse relation comes from the radial null condition. It determines a function of advanced time wherever the prescribed curve is differentiable and has positive radius.