Is there linear 'frame dragging'?

Question

Very massive objects cause the so called 'frame dragging' that can increase the speed of a beam of light to a total aggregate speed faster than the speed of light in normal circumstances so my question is: can a very massive fast object drag the'frame' along its trajectory so a theoretical space ship, chasing it, would have its speed increased due to this possible linear 'frame dragging'?

Answer 1

I don't see why the linear effect shouldn't be there. After all, you can envision the rotation as a following up of infinite linear motions. At any instant, a body in circular motion is composed of bodies with linear motion. If you envision two massive plates moving parallel through space. The plates are kept at rest wrt each other. Between the plates, there is no gravitation due to mass, but you will be dragged along in a direction parallel to the plates if you find yourself in between them (or outside them but in between you'll experience no "normal" gravity). You will end up with the same velocity as with which the plates are moving. This goes to show that space is connected to matter and not to mass, which is just a property of matter. If only mass were the cause of curvature, then no framedragging was present.

Answer 2

Consider an infinitely long cylinder that moves at some speed: does it drag test particles along?

We can move to the view from an observer moving along the cylinder at the same speed as the cylinder. The observer sees a static Levi-Civita spacetime outside the cylinder: $$ ds^2 = r^{8\sigma^2-4\sigma}(dr^2+dz^2) + D^2 r^{2/4\sigma}d\phi^2 -r^{4\sigma} dt^2 $$ where $\sigma$ and $D$ are constants, with $\sigma$ behaving like a mass density. Note that for a particle in this spacetime there is no acceleration along the z direction (e.g. the orbiting geodesics have constant angular velocity and remain in a plane). So there is no frame dragging in this view.

Moving back to the "stationary" view where we see the cylinder and previous observer sweep past, since it is related to our view by a Lorenz transformation along the cylinder, we reach the same conclusion. A bunch of particles orbiting in sync (say one with period twice the other) will have synced orbits in any of the other frames.

Compare this to Bonnor beam spacetimes, where parallel beams of light do not attract each other.