Warp drives and event horizons

[gpk]

Not entirely sure if this is the right section for this question.

Hypothetically, you can achieve FTL travel by bending spacetime around a spaceship ...

If such a device would be built ... would it be able to go past the event horizon of a black hole and then escape out of it? (I mean according to known laws ... not experimental evidence ;) )

 

[bcrowell]

Interesting question. If so, then I think it would effectively violate cosmic censorship. It would be very much like the examples in which it's claimed that you could overcharge a black hole and make it into a naked singularity -- see Veronika Hubeny, 1998 "Overcharging a Black Hole and Cosmic Censorship," http://arxiv.org/abs/gr-qc/9808043 .

 

[Simon Bridge]

Welcome to PF;
The warp bubble of something like an Albecuierre drive, is imposed on the existing spacetime - it works by changing the local geometry to suit itself.

As such a bubble approached the Schwarzschild radius, provided the bubble remained intact, the shape of the event horizon would change because the geometry is no longer spherical. The bubble would never actually cross the event horizon in the way you are probably thinking. Think of it as a large regular mass close to a large imaginary mass approach a black hole. The ship itself is inside the bubble and never even sees an event horizon.

But this is pretty off-the-cuff - with GR a lot depends on the details and I didn't actually do the math.
If someone would like to - that would be interesting - thanks in advance ;)

iirc: Being able to travel FTL would not necessarily allow escaping a black hole, as the common notion that a black hole merely possesses an escape velocity greater than c is not all there is to it.

I've had a look around and most answers online focus on the "FTL" aspect and miss the "changing the geometry of space-time" part of the drive... so you get replies like "all paths lead to the singularity" etc.

 

[PAllen]

Just to throw in my non-calculated intuition, I would think that an Alcuierre drive probably could have a trajectory entering and leaving the horizon (say, at a near grazing angle) of a super-massive black hole. This just based on the idea that locally, the horizon region is normal spacetime, and a warp drive follows can follow a spacelike trajectory quasi-locally, observed from the outside, and a spacelike curve can definitely enter and leave a BH.

 

[Simon Bridge]

I think we have to be careful to distinguish "event horizon" from "Schwarzschild radius" here though.

 

[K^2]

I think we have to be careful to distinguish "event horizon" from "Schwarzschild radius" here though.

Not in the way PAllen approaches it. Naturally, once you take into account the effect of whatever generates warp bubble on neighboring space-time, the ship can't be passing through an event horizon. But it will pass through the place it ought to be at, which still raises interesting questions. In particular, whether something else that fell in would be able to send a message to the ship.

This mirrors the talk on Alcubierre drive as a time machine somewhat, as it is all down to conditions under which a ship under warp drive can communicate with the world outside of the warp bubble. And there are obviously going to be limitations on that, but whether or not these will prevent cosmic censor from being violated, I have no idea. I'm sure somebody worked out the null geodesics for Alcubierre metric, but I haven't seen the results. That'd be the first step in sorting out this whole thing.

 

[yuiop]

At least some versions of the Alcubierre drive require external generators along the intended path to generate the bubble that carries the spaceship. These generators obviously could not be stationary below the Schwarzschild radius. However, it *may* be possible to drop the spaceship into the BH and then drop a series of these generators after it, which when switched on *may* be able to extract the spaceship back outside the Schwarzschild radius. A lot of detailed calculations would be have to be carried out, before anyone could be sure that was possible.

I've had a look around and most answers online focus on the "FTL" aspect and miss the "changing the geometry of space-time" part of the drive... so you get replies like "all paths lead to the singularity" etc.

As I discovered in the other Alcubierre FTL thread, the future light cone of a particle does not necessarily enclose the inevitable set of possible future events for the particle, because a warp drive is activated, it tilts the future light cone to point in a different direction.

 

[Simon Bridge]

We are getting dangerously into speculation land. These should help:
http://arxiv.org/pdf/1107.5650.pdf
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110015936_2011016932.pdf

 

[skylon7]

Based off of what I know about the Alcubierre drive, it pulls space towards the ship in whatever direction the ship faces. Like if the ship were going towards a star, it wouldn't pass the star unless the ship turned and went around the star. This is the problem with even horizons; they surround the black hole like a sphere. No matter which direction you face, you would be facing towards the event horizon, hence you could get infinitely close to it, but you can't escape it.

 

[PAllen]

Based off of what I know about the Alcubierre drive, it pulls space towards the ship in whatever direction the ship faces. Like if the ship were going towards a star, it wouldn't pass the star unless the ship turned and went around the star. This is the problem with even horizons; they surround the black hole like a sphere. No matter which direction you face, you would be facing towards the event horizon, hence you could get infinitely close to it, but you can't escape it.

That is false. First, the event horizon only has a global definition, and is not a detectable feature of spacetime at all. Secontly, if you know where it is, when outside it, there is direction away from and towards it. The same is true inside it, as readily seen in Kruskal coordinates. See my post #4 - I am convinced it is correct.

[edit: a little more on the interior: the topology of spacelike slice using th most common foliation is a S2xR. The R spatial direction is the extra (specelike) killing vector direction labeled as t in SC interior coordinates. The +t spacelike direction preserves the area of S2. But there is a spatial direction of increasing t combined with increase of S2 area, that goes toward and through the event horizon.]

 

[PeterDonis]

a spacelike curve can definitely enter and leave a BH.

But the ship inside the "warp drive" bubble does not follow a spacelike worldline. Its worldline is timelike. The "warp drive" changes the curvature of spacetime. So the answer to the OP's question as it is stated is "no"; the "warp drive" does not allow an object to travel on a spacelike worldline, which is what would be required to escape the event horizon. Instead, the warp drive changes the spacetime "shape" of the event horizon so that the worldline of the ship does not pass inside it, as K^2 says.

whether something else that fell in would be able to send a message to the ship.

This is still not possible, if by "fell in" you mean "fell below the actual event horizon"--i.e., the horizon location after taking into account the effect of the warp drive on the geometry of spacetime. The actual event horizon is still an event horizon.

If by "fell in", however, you mean "fell below where the horizon would have been without the warp drive being there, but still outside the actual horizon", then yes, it's an interesting question (and probably unanswerable without some heavy duty numerical simulation) what the conditions would be for a message to be received by the ship inside the warp bubble.

 

[PAllen]

But the ship inside the "warp drive" bubble does not follow a spacelike worldline. Its worldline is timelike. The "warp drive" changes the curvature of spacetime. So the answer to the OP's question as it is stated is "no"; the "warp drive" does not allow an object to travel on a spacelike worldline, which is what would be required to escape the event horizon. Instead, the warp drive changes the spacetime "shape" of the event horizon so that the worldline of the ship does not pass inside it, as K^2 says.

The ship follows a timelike world line, but the path of the bubble, viewed on a larger scale, is effectively spacelike. For a large BH, it could follow a path that went through where horizon would have been, and then out. Further, I suspect there could be trapped light between such a trajectory and the horizon. On the other hand, I certainly agree that the trajectory is modifying curvature such that the inside of the bubble is not inside the absolute horizon, by the definition of causal connection to null infinity.

 

[PeterDonis]

For a large BH, it could follow a path that went through where horizon would have been, and then out.

The problem is defining "where the horizon could have been" physically; it's not observable. Even if we assume that the original BH was perfectly spherical, so that the apparent horizon (which can be measured locally, by looking at the expansion of outgoing null geodesics) coincided with the event horizon, that would no longer be true once the effect of the warp drive was included (at least I don't think so). So there would be no way of telling, locally, "where the horizon would have been", and since wherever that is is no longer the actual horizon, there wouldn't be a way of telling globally either.

I suspect there could be trapped light between such a trajectory and the horizon.

"Trapped" temporarily, perhaps--I would have to take some time to think about where the apparent horizon would be in this case. But not trapped permanently, since it would still be outside the horizon.

 

[PAllen]

"Trapped" temporarily, perhaps--I would have to take some time to think about where the apparent horizon would be in this case. But not trapped permanently, since it would still be outside the horizon.

The horizon could be a genus 1 surface as the bubble is going through that settles back to S2 after. Then there could easily be eternally trapped light closer to distant objects than the bubble.

 

[PeterDonis]

The horizon could be a genus 1 surface as the bubble is going through that settles back to S2 after. Then there could easily be eternally trapped light closer to distant objects than the bubble.

If the light is "eternally trapped", then it's inside the horizon. I thought we were talking about light outside the horizon, but closer to it than the bubble.

In any case, as I said in an earlier post, I don't think we have the tools here to mathematically analyze this case, since AFAIK there are no exact solutions for it. So we (including me) are really just speculating.

 

[PAllen]

In any case, as I said in an earlier post, I don't think we have the tools here to mathematically analyze this case, since AFAIK there are no exact solutions for it. So we (including me) are really just speculating.

Agreed. But I'm extrapolating from a paper Bcrowell posted in a thread a while ago showing how several tachyon like features could be constructed with multiple warp drives with the ability of timelike curve to go from one to another. For example, arbitrary construction of CTC via analog of tachyonic anti-telephone (in the large it is an anti-telephone; internally, it is a CTC). They did the math, and made it seem like 'in the large' you can do with bubbles whatever you can with spacelike paths. They explicitly verified how a timelike curve gets from one bubble to another. The thrust was that if such bubbles could actually be realized, they would come with all the baggage tachyonic travel. And a tachyon path can definitely go into and out of a horizon.

[edit: but the rocket inside would never enter or leave the horizon because the bubble make a thin 'donut hole' through the horizon, such that the rocket is always outside the horizon]

 

[PeterDonis]

the rocket inside would never enter or leave the horizon because the bubble make a thin 'donut hole' through the horizon, such that the rocket is always outside the horizon

Yes, I'm not disputing that this is possible; I'm just trying to be precise about exactly what's happening (and this quote of yours does that). And I agree that, once you allow exotic matter into the picture (which you have to to make a "warp drive"), things can get very weird. Violating the energy conditions--don't try this at home.

 

[SlowThinker]

Suppose the warp drive can be turned off by moving the exotic and normal matter close to each other, and turned on by moving them apart.

Could the spaceship fall below the horizon, and then "turn on" the drive, moving the horizon below itself, and get out?
Is it even necessary to move the horizon all the way under the ship? It might be able to simply approach the horizon from below...

Generally I try to avoid discussions of the inside of BH, but this might illuminate some details of the "non-static" spacetime, over-infinite acceleration, and time dilation...

 

[PeterDonis]

Could the spaceship fall below the horizon, and then "turn on" the drive, moving the horizon below itself, and get out?

If it did this, then by definition it was never actually below the horizon. The horizon is globally defined; it takes into account the entire future of the spacetime. So if the warp ship does this at any point, and escapes, the horizon, globally, already takes that into account. (It's hard to describe all this without using confusing language; we need some new verb tenses.)

A better question might be whether the ship could fall below the apparent horizon (which is locally observable--it's the place where outgoing light no longer moves outward, locally), and then turn on the drive and move the apparent horizon below it. My guess is it probably could as long as it wasn't too far below the apparent horizon. But that's just a guess.