  The Eddington-Finkelstein metric is obtained from the Schwarzschild metric by
a change of the time variable. It is well known that a test mass falling into a
black hole does not reach the event horizon for any finite value of the
Schwarzschild time variable $t$. By contrast, we show that the event horizon is
reached for a finite value of the Eddington-Finkelstein time variable $t'$.
Then we study in Eddington-Finkelstein time the fate of a massive particle
traversing an Einstein-Rosen bridge and obtain a different conclusion than
recent proposals in the literature: we show that the particle reaches the
wormhole throat for a finite value $t'_1$ of the time marker $t'$, and
continues its trajectory across the throat for $t'>t'_1$. Such a behavior does
not make sense in Schwarzschild time since it would amount to continuing the
trajectory of the particle "beyond the end of time."
