No Passing Zone: Falling Into an Evaporating Black Hole

Abstract

We analyze the proper time experienced by a freely falling observer approaching a Schwarzschild black hole, and extend this analysis to a black hole governed by the Vaidya metric, which accounts for mass loss due to Hawking radiation. While the Schwarzschild solution allows an infaller to reach both the event horizon and singularity in finite proper time, we demonstrate that for certain evaporation functions—such as those describing Hawking radiation—the proper time required to reach the horizon diverges. Under these conditions, the black hole may evaporate entirely before the infaller arrives at the horizon, challenging conventional notions of event horizon formation and permanence.