system
Given the following post, respond as if you're commenting on Reddit:
human
Question about time at the Event Horizon of a Black Hole.

Gravitational time dilation states that time slows down in the presence of mass. In the extreme time (as observed from a remote location not affected by the gravitational field) stops for an object at the Event Horizon of a Black Hole. This is described as "From the point of view of a remote observer an object falling into a Black Hole takes an infinaite amount of time to pass through the Event Horizon".

However, the usual explanation if this that I have seen is that time does not slow down from the point of view of the falling object. From it's reference frame it passes through the horizon normally. Only an outside observer sees the time dilation.

My problem with this is that there is infinity involved. If, from the point of view of the outside observer, the object NEVER makes it through the horizon how can that be squared with the idea that from it's frame it proceeds normally?

Edit: Thanks for the replies. But none of them, so far, address the issue of infinity. It is like one point of view says Yes but another point of view says No. If it takes an infinite amount of time (from the view of an outside observer) that means it will never happen (No) but it does happen. How is this reconciled?

Also, if the object is "smeared" on the Event Horizon then it must lose its structural integrity. How can that be reconciled with the statement that "The transition from outside to inside is totally smooth."
gpt
That picture is essentially correct. There's nothing special about the event horizon as seen by an observer falling into the black hole. Time doesn't stop, it doesn't feel something new or exciting happening. The transition from outside to inside is totally smooth.

*But*, the horizon does have some funny properties, the most famous of which is that it's the point at which the escape velocity is the speed of light. This means that light can take a very, very long time to escape if it's emitted from a location very close to the horizon.

So let's say you have an astronaut falling into a black hole, emitting light pulses at regular intervals, according to her onboard clock. According to an outside observer observing these light pulses, the interval between these pulses gets longer and longer as the astronaut gets closer to the horizon and light takes more and more time to climb out of the gravitational field. Of course, that interval can get arbitrarily long, depending how close the astronaut is to the horizon when she sends her last signal before crossing the horizon.

So yes, there's an infinity for one observer, and a finite number for the other. And that's fine! Physics doesn't forbid that sort of thing. In particular it comes from the fact, crucial to relativity, that time isn't absolute. Time to two different observers can be two very different things, and as long as there isn't a contradiction when these observers go to compare their measurements (if they even can do that), then there isn't a problem.