I understand the equivalence of gravity and uniform linear acceleration. But I'm less clear on the example involving circular motion (merry-go-round) and the equivalence of gravity and centrifugal force, because I'm unclear about the connections between SR & GR. The example does illuminate certain points, like the sense in which standing on the earth's surface is a matter of constant "acceleration" away from the spacetime geodesic (because centrifugal force is really constant acceleration away from the direction perpendicular to radial). And of course it shows a connection between time dilation due to relative motion (faster motion away from center) and due to gravity. But is this connection an identity or an analogy? How does one get from Lorentz transformations to a curved spacetime metric in this example? It seems to me that the motion-based length contraction would drop out of consideration because it would be perpendicular to the radial direction. Then do the tidal forces produced in the "centrifugal field" somehow match or account for the difference between coordinate ("reduced circumference") and proper length in curved spacetime?