View from Infinity
To a distant observer, an infalling object appears to slow down as it approaches the horizon due to extreme gravitational time dilation. The object never seems to cross the horizon within finite coordinate time t, fading from view due to redshift.
View of the Infaller
For the infalling observer, crossing the horizon takes a finite amount of proper time. They notice nothing special locally at the horizon (assuming a supermassive black hole with weak tidal forces). They continue smoothly into the interior.
Resolving the Paradox
Distant Observer
- Sees object freeze at horizon
- Object redshifts to invisibility
- Never sees crossing occur
Infalling Observer
- Crosses horizon in finite proper time
- No local drama at horizon
- Proceeds to singularity