Acceleration does not wrap space..............
Paul
Ummm, well, actually it does.
Acceleration
WP: "With changing velocity, accelerated objects exist in warped space (as do those that reside in a gravitational field). Therefore, frames of reference must include a description of their local spacetime curvature to qualify as complete."
Let's say you don't like Wikipedia. Fine. Here's the deal: We define local spacetime curvature in an inertial frame as "flat." Objects moving at a constant velocity are inertial. To an observer who is in an accelerated frame of reference, such objects move not in a straight line, but in a curve. It is in fact the nature of accelerated frames of reference that
all inertial objects will move in curves with respect to them. Since we have already defined inertial motion as being in a straight line, and space in an inertial frame as flat, it follows that an accelerated frame must be a curved frame; otherwise, straight lines would still be straight, and they are not, they are curved. Observers in accelerated frames therefore observe spacetime curvature, because inertial objects move in curves. The degree of curvature of the frame's spacetime can be directly measured, by measuring the curvature of the motion of inertial objects in that frame.
But hang on a minute: to an observer motionless in a gravity field, all inertial motion is curved. Thus, it directly follows that for such an observer, spacetime is curved; and that curvature is called "gravity."
There is no difference between gravity and acceleration that cannot be explained by the fact that a gravity field is spherical. Locally, acceleration and gravity are
identical in every respect. That is the meaning of the equivalence principle.