Alcubierre Warp Drives and Strong Gravity Fields

[GeeKay]

Having only lately caught up with the ideas surrounding the Alcubierre warp drive concept, I am still struggling to understand how such a system would cope in regions of seriously non-flat spacetime - say, performing an otherwise lethally close "flyby" (excuse the grammatical hand-waving here) of a neutron star or stellar-mass BH. Reading between the lines from some online articles, none of which directly address this subject, the thought comes to mind such a spacecraft and its occupants would be unaffected by such an encounter while in warp mode, no matter how intense the gravitational tides might be. Nonetheless, the suspicion is that this may not be correct, though all this is way beyond my ken. Any ideas? 

[joigus]

2 hours ago, GeeKay said:

Having only lately caught up with the ideas surrounding the Alcubierre warp drive concept, I am still struggling to understand how such a system would cope in regions of seriously non-flat spacetime

What is your approach? General relativity does not satisfy the superposition principle, and it would take quite some work to see what would happen to this otherwise purely hypothetical configuration of extremely intense fields if the sources generating them got really close. Maybe @Markus Hanke can tell you more.

OTOH, there are practical reasons why you wouldn't wan to be anywhere near a NS or a stellar-mass BH, with their extremely gnarly accretion disks.

AAMOF, there are practical reasons why you wouldn't wanna be anywhere near a stellar anything. Even a heavy, whopping, magnetically-active planet could kill you. Example: Jupiter. Don't get anywhere near Jupiter unless you want to die fast.

[Markus Hanke]

10 hours ago, GeeKay said:

Having only lately caught up with the ideas surrounding the Alcubierre warp drive concept, I am still struggling to understand how such a system would cope in regions of seriously non-flat spacetime

That’s an excellent question.

First and foremost, the original Alcubierre metric requires that spacetime outside and inside the “warp bubble” is Minkowskian, and thus flat; it is only the “bubble wall” which exhibits non-trivial curvature. If you take away this condition of asymptotic flatness by allowing non-negligible background curvature, the Alcubierre metric is no longer a valid solution to the Einstein equations under those circumstances. This is because GR is a non-linear theory, so one can’t simply add metrics together and expect the result to again be a valid solution to the field equations. IOW, the warp bubble wouldn’t remain stable if it came under the influence of a gravitating body; you might suddenly get strong tidal forces acting on your ship, or the bubble might simply break down and disperse.

Which begs the question - is there any kind of topological construct that behaves similar to Alcubierre’s warp bubble, but can exist in the presence of strong background curvature? I don’t know the answer for sure, but potentially this is possible. But then, such a construct would depend on the specifics of the gravitational environment, so if it propagates from a region of strong curvature to a region that is nearly flat, it would almost certainly not remain stable, so you’d have the same problem.

So is it possible to have a warp bubble metric that remains stable irrespective of the gravitational background? Due to how the Einstein equations work, I would say almost certainly not.

What may be possible though is to find a specific warp metric for a specific flight path through a given, specific gravitational environment. You’d have to know where you want to start and where you want to end up, and the exact spacetime curvatures in all regions in between. If you then had a powerful enough computer, you could try and find a metric that describes a stable warp bubble propagating through this setup. You would have to perform this calculation anew for every journey you want to undertake, since it’s specific to the parameters describing each journey. It’s another interesting question to ask whether it is guaranteed that there always exists a solution; perhaps some routes cannot be flown at warp speeds…?

[Mordred]

Good answer Markus I can't think of anything to add +1

[GeeKay]

Markus, many thanks for your detailed responses - thought-provoking conjectures included! 🙂 The take-home message then is that flat spacetime is (as far as we can tell at present) an absolute prerequisite for this kind of warp-drive system, that any region exhibiting locally strong spacetime curvatures would therefore need to be avoided at all costs. Clearly then a fair amount of route planning (infrastructure too?) would be needed when it came to plotting flight paths between various star systems. . . challenges for posterity most likely, alas.       

PS. I personally found this link helpful for gaining a basic overview on the Alcuberrie warp drive and the problems it poses. I include it here for other armchair laypersons like myself coming to this subject cold.

https://theaeroblog.com/6-reasons-why-the-alcubierre-drive-or-warp-drive-is-not-possible-in-2023/

[swansont]

2 hours ago, GeeKay said:

Clearly then a fair amount of route planning (infrastructure too?) would be needed when it came to plotting flight paths between various star systems. . . challenges for posterity most likely, alas.   

It ain't like dusting crops, boy! Without precise calculations you could fly right through a star or bounce too close to a supernova and that'd end your trip real quick, wouldn't it?

Or so it was claimed, a long time ago (in a galaxy far, far away)

[exchemist]

On 7/15/2024 at 7:10 AM, Markus Hanke said:

That’s an excellent question.

First and foremost, the original Alcubierre metric requires that spacetime outside and inside the “warp bubble” is Minkowskian, and thus flat; it is only the “bubble wall” which exhibits non-trivial curvature. If you take away this condition of asymptotic flatness by allowing non-negligible background curvature, the Alcubierre metric is no longer a valid solution to the Einstein equations under those circumstances. This is because GR is a non-linear theory, so one can’t simply add metrics together and expect the result to again be a valid solution to the field equations. IOW, the warp bubble wouldn’t remain stable if it came under the influence of a gravitating body; you might suddenly get strong tidal forces acting on your ship, or the bubble might simply break down and disperse.

Which begs the question - is there any kind of topological construct that behaves similar to Alcubierre’s warp bubble, but can exist in the presence of strong background curvature? I don’t know the answer for sure, but potentially this is possible. But then, such a construct would depend on the specifics of the gravitational environment, so if it propagates from a region of strong curvature to a region that is nearly flat, it would almost certainly not remain stable, so you’d have the same problem.

So is it possible to have a warp bubble metric that remains stable irrespective of the gravitational background? Due to how the Einstein equations work, I would say almost certainly not.

What may be possible though is to find a specific warp metric for a specific flight path through a given, specific gravitational environment. You’d have to know where you want to start and where you want to end up, and the exact spacetime curvatures in all regions in between. If you then had a powerful enough computer, you could try and find a metric that describes a stable warp bubble propagating through this setup. You would have to perform this calculation anew for every journey you want to undertake, since it’s specific to the parameters describing each journey. It’s another interesting question to ask whether it is guaranteed that there always exists a solution; perhaps some routes cannot be flown at warp speeds…?

That's interesting. I have a feeling I have read sci-fi novels in which faster-than-light travel takes place, but is only possible once one gets well away from sources of gravitation like the sun. However I'm sure the stories I'm thinking of date from a time before Alcubierre. 

[MigL]

As absolutely flat ( Minkowski ) space-time is not realizable ( gravity has infinite range ), and only used to simplify calculations for 'nearly flat' space-time, the question then becomes what level of background space-time curvature can the Alcubierre metric support to still remain stable ?
If any background curvature renders it unstable, then Alcubierre is just mathematics without a physical application.

[StringJunky]

7 hours ago, MigL said:

As absolutely flat ( Minkowski ) space-time is not realizable ( gravity has infinite range ), and only used to simplify calculations for 'nearly flat' space-time, the question then becomes what level of background space-time curvature can the Alcubierre metric support to still remain stable ?
If any background curvature renders it unstable, then Alcubierre is just mathematics without a physical application.

So, what happens when it reaches the Planck limit?

[StringJunky]

5 hours ago, StringJunky said:

So, what happens when it reaches the Planck limit?

Scrub this. I'm mixing quantum with classical.

[Markus Hanke]

12 hours ago, MigL said:

the question then becomes what level of background space-time curvature can the Alcubierre metric support to still remain stable ?

Yes, another excellent question. The thing here is that the Alcubierre metric as a solution to the Einstein equations can in some global sense be considered, mathematically speaking, to be a modification of flat Minkowski spacetime; more precisely, it modifies its geodesic structure by mapping what are non-geodesic paths in ordinary Minkowski spacetime (ie events connected by space-like paths) into proper light-like geodesic paths in the presence of the warp bubble. IOW, the ship enclosed in the warp bubble follows a proper geodesic everywhere, but without the warp bubble, the same spatial trajectory could not be a geodesic. For this reason it’s actually meaningless to ask what level of background curvature the Alcubierre metric can tolerate - if the background outside the bubble isn’t Minkowski, there is no Alcubierre solution. IOW, you can’t construct an Alcubierre drive if there are other sources of gravity anywhere, just like you can’t ever have a proper Schwarzschild black hole in a universe that isn’t otherwise completely empty. So in that sense the Alcubierre solution is highly unstable.

Unfortunately the same is also true for all of the other known warp solutions to the Einstein equations, and there are a few of those by now. Most notably you have the Natario metric (a moving warp bubble but volume-preserving, ie without contraction and expansion regions), and the Lentz metric (a warp metric that does not require exotic matter, but is restricted to subluminal effective speeds). All of these require a Minkowski background; I’m not aware of any solutions that work generically irrespective of background curvature.

As I said before, I think one would have to work out a specific warp solution for a given, specific flight route and gravitational background; working the equations backwards, this would allow us to construct a specific (not necessarily unique) energy-momentum distribution to realise such a journey. This is mathematically difficult, but should be possible in principle, given enough computing power. But it would mean that there is no generic warp drive à la Star Trek, not even in principle; you’d have to re-configure the entire drive geometry for each individual journey you wish to undertake.

And of course then there’s the sheer amount of energy required for such a drive. To put it into perspective - the Lentz drive, which allows travel without exotic matter at subluminal speeds, requires the energy equivalent of ~1/10 solar mass to create a single bubble that can enclose a ship of approx ~100m length. Not very feasible or desirable, in my opinion.

19 hours ago, GeeKay said:

The take-home message then is that flat spacetime is (as far as we can tell at present) an absolute prerequisite for this kind of warp-drive system

Yes, pretty much. But again, this is for an Alcubierre warp drive - it may or may not be possible to construct other warp-like solutions that are not restricted in the same way. It’s hard to tell, due to the complexity of Einsteins equations.

17 hours ago, swansont said:

Without precise calculations you could fly right through a star or bounce too close to a supernova and that'd end your trip real quick, wouldn't it?

At least you’ve found a way to end the journey at all  Because I don’t see how such warp bubbles, once created, could be influenced (steered, decelerated,…) from the inside, where your ship is.

[Mordred]

 

6 hours ago, Markus Hanke said:

 

At least you’ve found a way to end the journey at all  Because I don’t see how such warp bubbles, once created, could be influenced (steered, decelerated,…) from the inside, where your ship is.

That's one of several known issues with the Alcubierre drive another being that such a warp bubble generates Gamma rays that even using subliminal velocity could eradicate life on the planet of origin and the planet of arrival.

Again not very practical.

Lol who one day someone might write a sci-fi novel with Alcubierre missiles.

Edited July 17 by Mordred

[MigL]

Thanks for the detailed explanation Markus.