The Black Hole Paradox: How Can Time Stop and Evaporation Occur Simultaneously?

Question

If time stops at the event horizon of a black hole, as predicted by General Relativity, then how can Hawking radiation cause the black hole to evaporate? Doesn't evaporation require the passage of time, contradicting the idea that time is frozen at the horizon?

Answer 1

The spacetime where time stops at the horizon is an eternal black hole which does not evaporate. Spacetimes with an evaporating black hole are considerably more complicated, and I am not aware of any analysis that shows time stops at the horizon in them.

How Can Time Stop and Evaporation Occur Simultaneously?

They do not. Time only stops in eternal black holes, and then only in Schwarzschild coordinates.

Evaporation only occurs in other spacetimes.

If time truly stops for an object at the event horizon, how can it still experience any physical processes at all?

Only Schwarzschild coordinate time stops at the horizon. The time that governs physical processes is proper time. Proper time does not stop at the horizon. Coordinate time is a mathematical convention. Physical processes do not depend on such conventions

Answer 2

Time does not stop. It stops for an observer at causal infinity. An infalling observer would reach the singularity in finite time.