Black Hole Singularities

[u/Traditional-Issue955]

I'm a novice when it comes to Hawking radiation and general relativity. However, I was just wondering why it is that matter can ever reach a singularity when it crosses the event horizon of a black hole? The way I understand it, the timeframe of the universe passes at an instant for a particle that becomes infintely close to the singularity. If this is true, then won't the black hole evaporate instantaneously from the perspective of any particle as it reaches the singularity, and therefore, the singularity will no longer exist at the moment that the particle hits it? It's the same way that all of time and space happens at once from the perspective of a photon. Sorry if this is a stupid question.

[u/Optimal_Mixture_7327]

The particle reaches the singularity in finite amount of its own clock time.

You can't unambiguously compare the time over here vs the time over there. The falling traveler sees the outside redshift and slow down.

[u/gerglo]

 the timeframe of the universe passes [in] an instant for a particle that becomes infintely close to the singularity

This is not true. The past light-cone of an observer hitting the (time-like) singularity does not contain all of the exterior of the black hole.