Warppunk Setting

[Lambda]

I might have just changed my mind about allowing gravy guns.

To what extent does the ability to warp space imply the ability to manipulate gravity? It seems like there's some distinction, since an orbital trajectory isn't an inertial reference frame -- that is, an object that's accelerating due to gravity isn't just following a locally straight line through curved space.

[linkhyrule5]

I might have just changed my mind about allowing gravy guns.

To what extent does the ability to warp space imply the ability to manipulate gravity? It seems like there's some distinction, since an orbital trajectory isn't an inertial reference frame -- that is, an object that's accelerating due to gravity isn't just following a locally straight line through curved space.

Nope. The founding principle of general relativity is that there is no such distinction; this is why inertial mass and gravitational mass are always identical. An orbiting mass is moving along a geodesic - the local equivalent of a "straight line."

I'm not sure why orbital trajectories being non-inertial implies a distinction between gravity and inertia, but at any rate - no, the relation between gravity and spacetime curvature is extremely simple. G = 8 pi T, where G is the tensor that describes a gravitational field and T is the tensor that describes the curvature of spacetime. Gravity is warped space, and you can write any acceleration in terms of warped space if you're willing to go to sufficiently extreme lengths.

[Lambda]

If an orbiting mass is traveling along a locally-straight line, then why doesn't a photon orbit a planet at the same altitude as a space station?

[linkhyrule5]

Mm.

I am not sure! I am very certain of my final answer because G=8pi T is a very famous result and my professor made a very big deal about inertial mass = gravitational mass, but the intervening steps are beyond my current education.

If I had to guess, I would say that for whatever reason you're working in a Hamiltonian phase-space instead of real space and moving at a different speed is equivalent to facing a different direction that is, you're forced onto a different geodesic. There are lots of different orbits passing through the same point with totally different characteristics, and for whatever reason a satellite moves in a straight line that is at an angle to the direction a photon moves. (But they're both "straight lines").

[Unbitwise]

Almost. It's not phase space — having your coordinates be (x, y, z, x', y', z') — but rather spacetime (x, y, z, t). Using those coordinates allows the “straightness of the line” to depend on velocity — since a different velocity will result in a different t for a given (x, y, z).

[Lambda]

And is it possible to curve spacetime in such a way that an initially stationary trajectory (changing value of t but not x, y, z) would, in the course of remaining a straight line, become nonstationary? And then it keeps moving as it emerges into unbent spacetime?

[Unbitwise]

If you mean without changing the curvature of space (i.e. changing the mass in the environment) that would be violating a symmetry/conservation law by making a particular time special. If you just mean “the only thing that affects the object is gravity”, that's easy to set up in a straightforward Newtonian way:

Let there be three masses labeled A, X, B, equally spaced in a line in otherwise-sufficiently-flat space, and initially motionless in our reference frame. A and B have the same mass.

Therefore, ignoring tides (that is, nonzero size of X), X is attracted equally to both and therefore does not accelerate.

Now blow up A, i.e. split it into two or more parts accelerating away from the vicinity (not in line with X and B). X's trajectory is now towards B. Blow up B an you have now obtained the “keeps moving in unbent spacetime” condition.

If you have $MAGIC which can create a curvature without corresponding mass, then you don't need A; just temporarily create the equivalent of B. And for more localized effect, create a dipole — that is, also have temporary A with effective negative mass. This would reduce the impact on farther-away objects. But if you have arbitrary control over the curvature of space, you don't absolutely need that and can just declare that the effect is of limited extent. And build the Alcubierre drive while you're at it.

[Lambda]

It seems reasonable to declare that the warp drive is an Alcubierre drive. I'm not sure I understood the rest of it.

"without changing the curvature of space": We're definitely changing the curvature of space? That's what the warp technology is.
falling towards B: That seems generally reasonable; you could certainly accelerate by shortening the distance to an existing heavy object in the direction you want to go. On the other hand, the warp drive doesn't necessarily shorten the entire distance to be covered at once, but rather just the section of "road" that's currently actually in use, so it might not have the range to make that practical.

I'm not completely convinced that creating a curvature is directly equivalent to creating a mass, in terms of making things fall.

[Unbitwise]

Sorry, I failed at disambiguation. By "without changing the curvature of space" I meant without making some change at the same time the motion starts. That is, there is no static configuration of curvature-of-space-around-a-mass which will cause the mass to start moving at some later time than when that configuration starts to exist. I don't think that's what you wanted, but I saw the possible meaning and wanted to avoid it.

[Lambda]

In that case, I think I can reasonably rule that it doesn't work because matter tends to resist warping of the space that it occupies. (Warp drive and shields only warp space around the ship. A ship using warp drive passes through warped space, but that space is already warped before the ship enters it.) You could, in theory, use the warp device to navigate within a system by adjusting your distance from (and therefore attraction to) the star, but this is usually not cost-effective in comparison to conventional reaction-mass engines.