# does a rotating moving body in “flat” space curve its path because of frame dragging?

I am not a physicist.

let's say we have a space with an object in it, where all other gravitational bodies are so far away that their affect on the shape of the space is negligible.

let's say the object is moving, and rotating such that we can say (for simplicity's sake) that it is moving to the right, and rotating clockwise (so we are considering rotation around the z axis, and movement in the x axis). therefore the +y side of the object is moving faster than the -y side of the object relative to the underlying space.

it seems to me that this object should experience frame-dragging between the body and the underlying space and so curve its path such that it appears to curve very very very slightly upwards in y.

is this correct?

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No, it's not correct. Let's assume the object is axially-symmetric for simplicity. If the object is light (so we can assume spacetime really is flat), then we can change to an inertial frame where its movement is, momentarily, purely rotation. Now it is obvious by symmetry that it is not going to start moving on any direction, because no direction is now preferred: in other words its movement in that frame is always purely rotation. The argument for a non-axially-symmetric object is more hairy (read: beyond me at this time of night) but similar. – tfb May 3 at 18:55