Affine-time scaling of a nonradial Schwarzschild photon plunge
= Affine-time scaling of a nonradial Schwarzschild photon plunge
{c}
{title2=$r\propto(\lambda_*-\lambda)^{2/5}$}
For nonzero angular constant $h$, the interior null radial equation gives $\dot r^2\sim2\mu h^2/r^3$. Its inward branch integrates to $r^{5/2}\sim\tfrac52\sqrt{2\mu}|h|(\lambda_*-\lambda)$. Thus the singularity is at finite <affine parameter> and $r\propto(\lambda_*-\lambda)^{2/5}$. The zero-angular-momentum case has a different affine scaling.