Hawking Evaporation is Inconsistent with a Classical Event Horizon at
  $r=2M$
  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.
