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

TL;DR

This paper argues that classical physics cannot reconcile black hole formation and evaporation times, implying the need for new physics or quantum effects to resolve the paradox of event horizon formation.

Contribution

It demonstrates that classical considerations lead to a paradox in black hole formation and evaporation, suggesting the necessity of quantum effects or new physics.

Findings

Classical analysis shows a cutoff outside the horizon is needed for consistent formation and evaporation times.

Several possible resolutions involve no horizon formation or quantum modifications to spacetime.

Classical physics alone cannot resolve the black hole information paradox.

Abstract

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.