Observing someone falling into a Black Hole.

Flatland

I understand that anything falling into black hole would appear to take forever to cross the event horizon relative to an observer at a distance. But what if you were hovering right above the event horizon and you saw someone fall in? Would they still appear to be frozen in time? If so what if you tried to shove them in?

zhermes

Even then it would appear to take forever. The gravitational time-dilation at the event horizon is a proper of the horizon itself---as viewed from any finite (non-zero) distance away, the effect becomes infinite as the infalling object approaches the horizon.

The particular conditions of infall (e.g. whether they are pushed or not) doesn't matter.

Flatland

So what if I was right behind him pushing him in as hard as I could? And also would I be able to communicate with the person falling in? And how long would I be able to communicate with him for since it takes him "forever" to fall in?

zhermes

It doesn't matter how hard you push him. As long as you are not falling in with him, he will appear to take forever to go in.

You can communicate with him---you can send signals to him (because signals can go INTO the horizon), but he won't be able to respond (signals can't come out).

While he 'appears' to take forever to fall in, he did actually fall in----from his perspective, he cross the event horizon without anything interesting happening.

Flatland

So initially I would receive his responses but not after he falls into the event horizon even though he appears to still be falling in?

zhermes

Yes.

The exact details are a little more complicated---but yes, that is the main idea.

Imagine he sends a signal towards you every second---from his perspective (his reference frame). From your perspective his signals get farther and farther apart, until there is an infinite amount of time between the signals----in this way, you only end up receiving a certain number of signals.
From his perspective, he eventually crosses the horizon, and even though he keeps sending signals every second---only a certain number of them were sent out before he crossed the horizon---and again only a certain number of signals end up getting out to you.

In this way, both reference frames agree on the number of signals that are received---this is an important aspect of maintaining physical symmetry.

Flatland

So what if I try to grab him at this point? Would he just be a hologram of sort?

zhermes

You wouldn't see him by the time you got there.
Even just reaching out your arm.

SHISHKABOB

a side question to falling into a black hole: the event horizon is a surface, right? If I watched someone fall into it, wouldn't their image become "flat"?

zhermes

Yes it would.

SHISHKABOB

So if someone were to take a close look at a black hole's event horizon, it would be a cluttered flat image of everything that ever struck the surface, right? Assuming that the black hole existed in an environment with a lot of stuff falling onto it.

whoah and wait, if something at the event horizon appears to take forever to continue falling inwards, what happens to the light that is bouncing off of an object falling onto the event horizon?

alexg

If I'm remembering correctly off the top of my head, this is Steven Hawking's current argument for why information is not destroyed when it falls into the BH.

Chronos

The infalling observer has the same problem as the stationary observer. The stationary observer also becomes frozen from the perspective of the infalling observer as he reaches the event horizon, so, neither can communicate with the other. Photons from outside the EH cannot catch up with the infalling observer as he reaches the EH.

Flatland

I'm not quite sure I understand this. I'm assuming you mean that the light is being red shifted but wouldn't you be able to see him with sensitive enough equipment?

DaveC426913

He would eventually be infinitely red-shifted. i.e. the photon's energy would approach zero, its wavelength would approach infinity.

Flatland

Does it actually become infinitely red-shifted after some finite time or does it only approach infinity?