So I have the metric as ##ds^{2}=-(1-\frac{2m}{r})dt^{2}+(1-\frac{2m}{r})^{-1}dr^{2}+r^{2}d\Omega^{2}##*
I have transformed to coordinate system ##u,r,\phi, \theta ##, where ##u=t-r*##(2),
where ##r*=r+2m In(\frac{r}{2m}-1)##
and to the coordinate system ##v,r,\phi, \theta ##,
where...