Concerning gravitational time dilation in artificial gravity (made by a rotating torus like in many sci-fi movies) how would you go about calculating the effect?
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Since there is no excess mass, there is no deformation of spacetime and thus no gravitational time dilation. However, since there is a velocity there is a special relativistic time dilation. Particles going around in circular accelerators only experience special relativistic time dilation.
The time dilation from the motion will be equivalent to a gravitational time dilation with effective mass of $M_{eff} = \frac{v^2r^2}{G}$ (where r is the radius of the rotating torus). And there is a major difference between this time dilation and the usual special relativity time dilation with inertial frames. Since anyone or thing in the torus is undergoing constant acceleration it is constantly changing inertial frames. This motion is therefore not relative and the clocks in the non-rotating frame appear to the entities in the rotating frame to be going faster. Thus, when a twin leaves the rotating frame, he/she will actually be younger than the stay at home twin.
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