Horizon redshift of a Schwarzschild infaller
= Horizon redshift of a Schwarzschild infaller
For smooth radial infall through a future <Schwarzschild event horizon>, outgoing retarded time obeys $u\sim-4M\log(\tau_H-\tau)$. A distant observer sees the <redshift> grow as $e^{t_{\rm rec}/(4M)}$. Its exponent in emission <Schwarzschild time> is instead $1/(2M)$, because $t_{\rm rec}\sim2t_{\rm em}$. At finite fixed observer radius the wavelength ratio includes $\sqrt{1-2M/r_B}$.