Black Holes & Warp Bubbles - Event Horizon Considerations

[bob012345]

TL;DR

A question regarding Alcubierre Warp Bubbles and black hole event horizons. Would a warp bubble moving faster than c have a different effective event horizon?

Last night PBS showed two shows on Black Holes. In the shows the host traveled on a supposed warp drive spaceship. A question occurred to me. Suppose for the argument that the Alcubierre drive were possible. Then suppose you were in a ship contained in a warp bubble moving through space at say 10c. Now consider that warp bubble with respect to the event horizon of a black hole. We know anything moving at c (radiation) or below must not cross the event horizon. But what of our warp bubble moving at 10c? Would it have a smaller effective event horizon? Thanks.

 

[PeterDonis]

what of our warp bubble moving at 10c? Would it have a smaller effective event horizon?

The interpretation of a warp bubble as "moving faster than c" assumes that the rest of the spacetime is flat. Obviously that is not true if the bubble is inside a black hole.

Since the EFE is nonlinear, I don't think a simple superposition of the two solutions, which is basically what your reasoning amounts to, is valid. One would have to simulate the combined solution numerically (unless a closed form expression for it could be found, which I think is highly unlikely) to see what the actual causal structure was. I would expect it to be different from the case of an ordinary test object inside a black hole, but I'm not sure the difference would be as simple as you describe.

 

[PeterDonis]

Would it have a smaller effective event horizon?

It's also worth noting that the term "event horizon" means the boundary of the region of the spacetime that cannot send light signals to infinity. If a warp bubble is present, that region could change. That wouldn't change the "effective" event horizon; it would change the event horizon, period; the event horizon would no longer just be spherical, it would have a very weirdly-shaped portion inside the spacetime "world tube" occupied by the bubble.

 

[bob012345]

The interpretation of a warp bubble as "moving faster than c" assumes that the rest of the spacetime is flat. Obviously that is not true if the bubble is inside a black hole.

Since the EFE is nonlinear, I don't think a simple superposition of the two solutions, which is basically what your reasoning amounts to, is valid. One would have to simulate the combined solution numerically (unless a closed form expression for it could be found, which I think is highly unlikely) to see what the actual causal structure was. I would expect it to be different from the case of an ordinary test object inside a black hole, but I'm not sure the difference would be as simple as you describe.

Thanks. But I didn't offer any reasoning or make any assumptions. I merely asked the question.

 

[PeterDonis]

I didn't offer any reasoning or make any assumptions. I merely asked the question.

The question you asked does implicitly make assumptions: for example, that "warp bubble moving at 10c" is even a meaningful description if the bubble is inside a black hole. It might not be. The only way to know would be to solve the EFE for this case; AFAIK nobody has done that. I don't think heuristic reasoning will do.

 

[bob012345]

It's also worth noting that the term "event horizon" means the boundary of the region of the spacetime that cannot send light signals to infinity. If a warp bubble is present, that region could change. That wouldn't change the "effective" event horizon; it would change the event horizon, period; the event horizon would no longer just be spherical, it would have a very weirdly-shaped portion inside the spacetime "world tube" occupied by the bubble.

Thanks. What you said is basically what I meant. The event horizon might be different when it interacts with the warp bubble. Perhaps the warp bubble doesn't end up inside the new event horizon even if a "classical" intersection would have suggested it might.

 

[bob012345]

The question you asked does implicitly make assumptions: for example, that "warp bubble moving at 10c" is even a meaningful description if the bubble is inside a black hole. It might not be. The only way to know would be to solve the EFE for this case; AFAIK nobody has done that. I don't think heuristic reasoning will do.

Thanks. I meant if it was approaching the black hole from far away at 10c. The whole question was about what happened when they interact. But you answered my question by saying the answer isn't obvious and requires detailed calculations.
Thanks again.

 

[PeterDonis]

I meant if it was approaching the black hole from far away at 10c.

But that is a different question. The event horizon, which is what you asked about in your OP, doesn't affect objects going into the hole. It only restricts objects going out of the hole.

The detailed "trajectory" of a warp bubble for any set of initial conditions would be expected to be different from that of an ordinary object. But that in itself doesn't have anything to do with the event horizon. (And of course it would need detailed calculations for any set of initial conditions.)