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

Infall time in the Eddington-Finkelstein metric, with application to Einstein-Rosen bridges