[IntronExon]

There are two frames of reference here, and only from the frame of the external observer does what you say hold true. From the point of view of infalling mass, there is no “freeze-frame” and time proceeds normally. The classic example to illustrate this is a black hole with so much mass that you can fall past the event horizon without experiencing significant tidal forces. You could survive the fall, Andy live for hours inside the hole before tidal forces turned you into subatomic sphagetti.

[olegkikin]

But from our perspective, the outside observers, why do black holes gain mass? It would take an infinite amount of time from our perspective for any mass to even touch the event horizon.

[IntronExon]

At this point a few issues arise. The first is that what you’re describing is a feature of the Schwarzschild metric, which applies to a model black hole, which is time-independent and eternal. There is no particular reason to believe that this accurately describes black holes in nature. For example this metric can not describe the merger of two black holes, but we now have observational evidence that this does indeed take place.

The biggest issue, aside from the model, is that time dilation is something which only matters when two observers “compare clocks.” Neither observer alone ever experiences a difference. The crew of a 99.9% lightspeed ship doesn’t experience time dilation... until they return home. It makes no sense to talk about the effects of time dilation from the point of view of a one-way trip to the event horizon.

[olegkikin]

> The crew of a 99.9% lightspeed ship doesn’t experience time dilation until they return home.

That's not true. They see the universe around them moving much faster.

Time dilation has nothing to do with "returning home".

[wallace_f]

I've never been able to feel comfortable understanding reference frames. Even considering simpler examples: So what if a probe is launched to catch our solar system's recent cigar-shaped visitor. Assume we catch it and want to bring back a sample of equal mass to the probe. So what determines the kinetic energy required to return this sample to earth? Is the delta relative to that of the probe, to the solar system, or to its origin? What if it is was accelerated to 0.1c relative to its launch site in another galaxy, but is only travelling at 0.001c relative to us?

Common sense dictates that the probe and the sample would require equal fuel to return to earth; but to an observer riding this cigar-rock, why would the universe cut our probe some slack if we changed its kinetic energy rather than the observer?

[IntronExon]

It’s from the frame of reference of the probe you make fuel calculations. The various observers don’t necessarily need to agree on the ordering of events (Relativity of Simultaneity), but they will always agree on the laws of physics, which are the same everywhere. If it takes a given amount of fuel to accelerate a mass to a given degree, everyone will agree on that point. It might take som calculation to make that clear to all of the observers, but they will agree regardless if some are in accelerating reference frames, and others inertial.

[IntronExon]

Seeing the universe around them is comparing clocks with another frame of reference. On the ship, life at 99.9% and life at 1% of c is identical. By the same token, if you fell into an (inactive) supermassive black hole, your watch would trick the same way into and past the event horizon. You would in fact live inside the hole for hours until you were torn asunder.

[simonh]

The point is, the crew onboard the ship can compare clocks with those in different frames of reference at any time. All they have to do is observe the period of a pulsar for example, or measure the orbits of binary star systems, etc. It would be quite apparent to them that there is a time dilation effect for them with respect to most of the rest of the universe. See Tau Zero, by Poul Anderson. It has a few mistakes, but it's still a great read.

[IntronExon]

I’m not claiming that they can’t recognize that their relative velocity is much greater than their surroundings. You can even calculate the degree of time dilation you’re experiencing relative to another observer, but I’m not talking about that either.

The biggest issue, aside from the model, is that time dilation is something which only matters when two observers “compare clocks.” Neither observer alone ever experiences a difference. The crew of a 99.9% lightspeed ship doesn’t experience time dilation... until they return home. It makes no sense to talk about the effects of time dilation from the point of view of a one-way trip to the event horizon.

That has to do with the experience of their frame of reference. Time does appear to “slow down” for them, rather everything else will seem to “speed up.” You can infer the difference, but you can’t sctually communicate that or compare with anyone else until you decelerate. In the extreme case of a gravitational event horizon, there will be no ability to ever communicate again. The fact that external observers will see you infinitely redshifted doesn’t imply anything about your experience of subjectively falling past the horizon. Both are valid frames of reference, but ultimately will develop spacelike separation which prohibits further communication.

As it relates to the issue st hand, you can’t make accurate statements about mass never passing through the EH based on observations from a distant from of reference.

[shullbitt0r]

> Seeing the universe around them is comparing clocks with another frame of reference

So, if you don't sense anything, you don't sense time dilation either?

This is slightly more complicated. First of all, you haven't given a frame of reference. If you claim someone were moving at 0.99c then you have already set the frame of reference. And they would have to gain near infinite mass and would die. You seem to assume a restricted frame of reference though, inside the spaceship. So, a point of reference inside the spaceship would see light moving with c inside the spaceship. And would assume his own point of reference as the origin of the inertial frame of reference. So baring any outside measurement, how do you know the spaceship is moving with 0.99c and in which frame of reference?

[shullbitt0r]

Oops: I notice my mistake now, acceleration is the problem, not speed.

[xelxebar]

I just wanted to mention that the Schwartzchild metric doesn't only apply to black holes. It's the general metric for a spherically symmetric, static space-time, so it's good for roughly spherical bodies like stars and planets over small timescales.

Recently, I worked out the ISS orbit using the Schwartzchild metric as an approximation of Earth. It's cool to see the orbital period pop out and agree with real life! It's then just a small step to calculate the time dilation experienced by ISS astronauts.