$\tau =\int \frac{dr}{\sqrt{\frac{2M}{\tau +x}-\frac{2M}{R}}}=\sqrt{\frac{R^3}{8M}}\left[2\sqrt{\frac{r}{R}-\frac{r^2}{R^2}}+{\cos }^{-1}\left(\frac{2\tau }{R}-1\right)\right]$