A simple classical consideration of black hole formation and evaporation times focusing solely on the frame of an observer at infinity demonstrates that an infall cutoff outside the event horizon of a black hole must be imposed in order for the formation time of a black hole event horizon to not exceed its evaporation time. We explore this paradox quantitatively and examine possible cutoff scales and their relation to the Planck scale. Our analysis suggests several different possibilities, none of which can be resolved classically and all of which require new physics associated with even large black holes and macroscopic event horizons:(1) an event horizon never forms, for example due to radiation during collapse (resolving the information loss problem), (2) quantum effects may affect space-time near an event horizon in ways which alter infall as well as black hole evaporation itself.
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