Ingoing Eddington-Finkelstein coordinates
= Ingoing Eddington-Finkelstein coordinates
{c}
The advanced coordinate $v=t+r_*$ puts the radial Schwarzschild metric into the form
$$
ds^2=-\left(1-\frac{2M}{r}\right)dv^2+2\,dv\,dr+r^2d\Omega^2,
$$
which is regular at the future horizon.
These are the advanced, ingoing member of the <Eddington-Finkelstein coordinates>.