Some "Easy" stuff about black holes

[Diadem]

How can you be a free falling observer in a spaceship with non-zero dimensions? Different parts of the spaceship will be in different inertial frames, so for the spaceship to remain in one piece they can't all be free falling.

It's been a while since I did my course on black holes though. I'm a bit rusty. A sufficiently big black hole will have negligible tidal forces, so we can ignore them for our calculations. But clearly if you stick part of a spaceship through the event horizon, that part of the ship can't get back. So if you then reverse thrusters, and fly out, clearly something must happen. I'd have to think a while to remember what though.

[Yakk]

So the thought experiment would go like this.

You have a ship. It has two clocks on it that broadcast a signal. One at the front, and one at the back.

You send it down the black hole. It thrusts away from the black hole, crossing the event horizon (as far as it is concerned) as slow as it wants to.

We define "crossing the event horizon" as "the clock tick at the front of the ship is never sent, while the same clock tick at the back of the ship does".

The ship is able to calculate what clock tick that will be, given a deterministic trajectory, so it "knows" when it crosses the black hole.

When it crosses the black hole, it activates its thrusters. Space is locally flat, so there is nothing pulling the ship apart. But the front of the black hole can never exit the event horizon, yet the back of the ship can?

I suspect the answer might be something tricky, like the cumulative tidal stress causes enough time warping so that the clocks "get out of sync" as far as a member of the crew is concerned. So as far as they are concerned, the back clock ticks before the front clock tick, so it isn't possible to thrust after the back clock tick and before the front clock tick.

[starslayer]

How can you be a free falling observer in a spaceship with non-zero dimensions? Different parts of the spaceship will be in different inertial frames, so for the spaceship to remain in one piece they can't all be free falling.

It's been a while since I did my course on black holes though. I'm a bit rusty. A sufficiently big black hole will have negligible tidal forces, so we can ignore them for our calculations. But clearly if you stick part of a spaceship through the event horizon, that part of the ship can't get back. So if you then reverse thrusters, and fly out, clearly something must happen. I'd have to think a while to remember what though.

I suspect it matters where the thrusters are/where exactly the force is acting. If the thrusters are on the front of the ship/have crossed the event horizon, nothing much bad happens. If they're outside the event horizon though, the ship will tear itself apart. The tension forces fly off to infinity, because the back of the ship ends up trying to move at greater than c relative to the front of the ship.

[eSOANEM]

How can you be a free falling observer in a spaceship with non-zero dimensions? Different parts of the spaceship will be in different inertial frames, so for the spaceship to remain in one piece they can't all be free falling.

I started with a line the ends of which were space-like separated and then allowed each end to fall in separately. Essentially it's a ship made of jelly.

It's been a while since I did my course on black holes though. I'm a bit rusty. A sufficiently big black hole will have negligible tidal forces, so we can ignore them for our calculations. But clearly if you stick part of a spaceship through the event horizon, that part of the ship can't get back. So if you then reverse thrusters, and fly out, clearly something must happen. I'd have to think a while to remember what though.

It's late again so I can't really sketch the diagram now, but I'll have a go tomorrow and see if I can get a rough idea (although to get a sensible answer out, I think I'll need to assume the ship is actually two separate infinitely rigid bodies).

In essence, I'd need to tear it apart as starslayer said.


...


Edit: Not actually drawn the diagrams. Just visualised in head instead. Should be as good as sketch.

Exact behaviour will depend on the rigidity of the spaceship. For an infinitely rigid ship (by which I mean one for which the space-like separation between the two ends at a given point in time (as determined by parallel transport) is constant), the front will pull the back in no matter how strong the engines are.

For a finitely rigid but unbreakable ship, it will stretch out arbitrarily far (assuming it's made of some continuous bulk material rather than actual particles) although I think this stretching will lead to additional matter falling in as, for it to stretch, the material closer to the horizon must be moving away from it slower than the rest so, if the rest is just escaping, some of it must still fall in. Iterating this process, the ship will still get pulled in eventually, it will just take longer and will go in a lot thinner than it otherwise would.

For a more realistic ship which can be snapped, ~1/2 would escape although the less rigid the materials are, the less will escape (for the same reason the ship described above will never escape).

This question is somewhat similar to one I posed a while ago on the relativity thread about trying to break colour charge confinement by aiming a meson at an event horizon such that one quark falls in and the other doesn't (although thinking about all this black holes stuff's made me think that it won't work even neglecting quantum effects because, for it to dip in the horizon, it would have to be at c which is can't be).

[SU3SU2U1]

For an infinitely rigid ship...

Can't exist. See http://en.wikipedia.org/wiki/Bell's_spaceship_paradox and http://en.wikipedia.org/wiki/Born_rigidity

[Diadem]

For an infinitely rigid ship...

Can't exist. See http://en.wikipedia.org/wiki/Bell's_spaceship_paradox and http://en.wikipedia.org/wiki/Born_rigidity

Well, you can always reroute power from the main deflector dish to reinforce hull integrity. That should do the trick.

[eSOANEM]

For an infinitely rigid ship...

Can't exist. See http://en.wikipedia.org/wiki/Bell's_spaceship_paradox and http://en.wikipedia.org/wiki/Born_rigidity

Yeah, I played around with the wording in that post a few times, one of which made reference to infinite rigidity being impossible. I was taking a born-rigid ship and putting it in the field. This seems kosher because no torque is being applied and, unlike Bell's spaceship, the two ends are trying to accelerate in different directions. That said, my ship still probably violated SR by having a superluminal speed of sound although I'm not certain.

[PM 2Ring]

Nice thread. I just have a few vaguely relevant comments.

When discussing black holes, please bear in mind that the basic Schwarzschild BH is a rather artificial entity: it's eternal, and it's the only "object" existing in its universe.

Yes, you can see the outside universe from within the EH of a BH, but the view isn't exactly normal: most of the light trajectories get rather bent as they fall into the BH, and the light gets extremely blue-shifted.

What Wikipedia has to say about the Bogoliubov transformation at the heart of the Unruh effect and Hawking radiation: http://en.wikipedia.org/wiki/Bogoliubov_transformation
And a nice thread on this topic from Physics Forums. Post #15 is especially good.
http://www.physicsforums.com/showthread.php?t=253478
TL;DR:
Bogoliubov transformations aren't actually about virtual particle - antiparticle pairs. They're a way of analysing systems composed of many particles that interact strongly with each other. Such interactions normally makes systems with multiple particles hard to analyze: the QM equations become very hard to solve. The Bogoliubov transformation allows you to mathematically "convert" the particles in the system into pairs of complementary quasiparticles that don't have strong interactions, apart from the interaction between the two quasiparticles comprising a given pair. This transformation is frame-dependent, so different observers will calculate different sets of quasiparticles and thus they will disagree on what particles are present in the Hawking or Unruh radiation.

Speaking of Hawking radiation, although it would be strong for mini black holes (if such things can exist) it's very weak even for stellar black holes, with a temperature in the microkelvin range; for galactic core BHs, it's in the nanokelvin range and smaller. This makes it rather difficult for an observer to detect. And until the CMBR gets much colder than its current value stellar & galactic BHs the outgoing Hawking radiation will be swamped by the incoming CMBR.

As has been mentioned several times in this thread, material approaching the EH of a BH never appears to cross it in the frame of a distant observer. Consider that this also applies to the original matter that collapsed to form the BH, so from the POV of the infinitely distant observer the BH takes an infinite amount of time to form...

Finally, on travel inside rotating black holes: it's possible for bodies to "orbit" inside a Kerr black hole. The position of bodies following such trajectories is not periodic in time (but the momentum is, IIRC). See http://www.technologyreview.com/blog/arxiv/26626/

[doogly]

Yes, the ubiquity of the naive particle - antiparticle heuristic is quite puzzling to me. No derivation of the Hawking effect has anything to do with them. And there are others beside the BT proof - but NONE of them reference pair production.

[eSOANEM]

Noted. I'll try to remember the Bogoliubov transformation for future discussions.

I also have a new question. Earlier in this thread I made reference to looking at some problems diagrammatically and now I'm starting to have doubts about the method by which I did it.

About 6 months ago, I finished reading the road to reality by Roger Penrose and, in it, I seem to remember him having a diagram showing a gravitational field by a series of rotated local lightcones (each effectively being a zoomed in view of the locally flat space which is equivalent to Minkowski space).

In my recent approach to the problems in this thread, this is what I tried, I assumed that the horizon stayed in the same place, started with a vertical lightcone and then gradually rotated it onto its side until the outwards null ray was vertical (compared to the distant lightcone) which, I think, should define the horizon (I then continued to rotate it a bit further for the ship part-way over the horizon problem).

I was having some doubts as to whether this can work because such a system produces null rays near to the horizon which, to an external observer would appear to be superluminal. I think this effect should be cancelled out by the fact that the null rays reaching out of the system to show the observer this would appear subluminal and so, the information would not be seen as moving faster than light globally and, locally, would not be.

Is this understanding correct, or this method of looking at the problem diagrammatically flawed?

[PM 2Ring]

About 6 months ago, I finished reading the road to reality by Roger Penrose and, in it, I seem to remember him having a diagram showing a gravitational field by a series of rotated local lightcones (each effectively being a zoomed in view of the locally flat space which is equivalent to Minkowski space).

[...]

I was having some doubts as to whether this can work because such a system produces null rays near to the horizon which, to an external observer would appear to be superluminal. I think this effect should be cancelled out by the fact that the null rays reaching out of the system to show the observer this would appear subluminal and so, the information would not be seen as moving faster than light globally and, locally, would not be.

You can't just linearly extend the rays from your light cones outside of their little locally (approximately) flat patch of Minkowski spacetime, and close to the EH those flattish patches can get very small, especially for small black holes. However, if you change coordinates you can make more useful diagrams of what's going on over extended regions. See http://en.wikipedia.org/wiki/Rindler_coordinates

[eSOANEM]

You can't just linearly extend the rays from your light cones outside of their little locally (approximately) flat patch of Minkowski spacetime, a

Of course. The paths will bend so they always follow (locally) the null cones. I was more worried about the possibility of a distant observer seeing superluminal transfer of information take place between two observers near the horizon than for the information to be passed to the distant observer.