Crossing an event horizon

[Bullgrit]

Am I understanding this correctly?

"Traveller" is moving towards an event horizon.

"Observer" is watching the Traveller.

The Observer sees the Traveller approaching the event horizon, but the Traveller slows, slows, slows such that although he is still moving towards the horizon, he never actually crosses it.

The Traveller sees himself approaching the event horizon, and crosses it with no slow down.

Is this an accurate description?

If so, does the Traveller actually cross the horizon? And when does he cross it -- at the "end of time"?

Bullgrit

 

[Plane Sailing]

The Astrophysics Spectator agrees with you

The Astrophysics Spectator: Falling through the Event Horizon of a Black Hole

Cheers

 

[Deset Gled]

The Observer sees the Traveller approaching the event horizon, but the Traveller slows, slows, slows such that although he is still moving towards the horizon, he never actually crosses it.

The Traveller sees himself approaching the event horizon, and crosses it with no slow down.

Is this an accurate description?

It's a good description for a sci-fi book. As is often the case with sci-fi physics, the real math gets in the way.

The bottom line is that you can't actually travel at the speed of light. If you could somehow travel faster than the speed of of light, lots of funny things would happen, but it is not an actualizable consequence.

The equation for time dilation is:

To = Tt / (sqrt(1-v^2/c^2))

Where To is time seen by the observer, Tt is time seen by the traveller, v is velocity of the traveller relative to the observer, and c is the speed of light.

The key point to notice in this equation is that when v = c, you literally divide by zero. Once you figure out how to do that, feel free to re-write math and/or physics as we know it. A similar problem happens when you look at inertial dilation, as your mass becomes infinite at the speed of light.

 

[Bullgrit]

The Astrophysics Spectator agrees with you

Reading that brings up another question that twists my noodle:

Two travellers moving towards the event horizon. (Maybe one slightly ahead of the other?) Traveller 1 sees Traveller 2 slowing and never reaching the horizon, but sees himself going through?

But back to the OP: When does the Traveller cross the horizon? At the "end of time" or some such?

The idea of something stretching to infinity, I can metally grasp, even if in theory. But something happening at infinity, well, that's getting me. Like climbing over an infinitely high wall.

Bullgrit

 

[El Mahdi]

Only Stephen Hawking truly knows...

 

[Deset Gled]

Two travellers moving towards the event horizon. (Maybe one slightly ahead of the other?) Traveller 1 sees Traveller 2 slowing and never reaching the horizon, but sees himself going through?

Well, you already know my stance on the fact that reaching the event horizon won't actually happen, but the equation I posted above tells you exactly what happens as two observers get near the speed of light.

Note that v is the velocity between the observer and the traveler, not relative to an absolute point (which, by the way, doesn't exist). If the observer is accelerating just a bit behind the traveller, it will look the same as if the traveller was accellerating slowly. To figure out how this looks to another non-accelerating observer, simply use a third person (second observer) to calculate the time dilation relative to both travellers.

 

[Umbran]

But back to the OP: When does the Traveller cross the horizon? At the "end of time" or some such?

In this case, the question of "when?" must be accompanied by "according to whose clock?"

By the Traveller's clock, they cross the event horizon whenever they should have, as a freely falling object - probably about 20 minutes past Noon.

By the Observer's clock, it is, "at the end of time or somesuch". Honestly, long before the end of time, light coming off the Traveller to the Observer will be so red-shifted as to be undetectable by the Observer.

This is assuming a fairly large black hole, without much tidal distortion near the event horizon. For smaller black holes, both the Traveller and the Observer see the Traveller turned into spaghetti long before the end of time.

 

[Umbran]

Well, you already know my stance on the fact that reaching the event horizon won't actually happen, but the equation I posted above tells you exactly what happens as two observers get near the speed of light.

Note that to cross the event horizon, the Traveller does not need to be moving near the speed of light.

 

[Deset Gled]

Note that to cross the event horizon, the Traveller does not need to be moving near the speed of light.

Thus demonstrating that I can remember formulas from my modern physics courses, but not simple terminology like "event horizon".

Carry on, nothing to see here.

 

[Klaus]

Reading that brings up another question that twists my noodle:

Two travellers moving towards the event horizon. (Maybe one slightly ahead of the other?) Traveller 1 sees Traveller 2 slowing and never reaching the horizon, but sees himself going through?

But back to the OP: When does the Traveller cross the horizon? At the "end of time" or some such?

The idea of something stretching to infinity, I can metally grasp, even if in theory. But something happening at infinity, well, that's getting me. Like climbing over an infinitely high wall.

Bullgrit

Maybe the Observer never sees the Traveler entering the Event Horizon because the *image* of the Traveller (ie, light bouncing off the Traveller and into the Observer's eyes) can't escape the Event Horizon, thus freese-framing the Traveller's image?